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Erschienen in: Engineering with Computers 2/2016

01.04.2016 | Original Article

Local integration of population dynamics via moving least squares approximation

verfasst von: E. Shivanian

Erschienen in: Engineering with Computers | Ausgabe 2/2016

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Abstract

This paper applies an approach based on the Galerkin and collocation methods so-called meshless local Petrov–Galerkin (MLPG) method to treat a nonlinear partial integro-differential equation arising in population dynamics. In the proposed method, the MLPG method is applied to the interior nodes while the meshless collocation method is used for the nodes on the boundary, so the Dirichlet boundary condition is imposed directly. In MLPG method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. The moving least squares approximation is proposed to construct shape functions. A one-step time discretization method is employed to approximate the time derivative. To treat the nonlinearity, a simple predictor–corrector scheme is performed. Also the integral term, which is a kind of convolution, is treated by the cubic spline interpolation. Convergence in both time and spatial discretizations is shown and more, stability of the method is illustrated.

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Literatur
1.
Zurück zum Zitat Apreutesei N, Bessonov N, Volpert V, Vougalter V (2010) Spatial structures and generalized travelling waves for an integro-differential equation. Discrete Contin Dyn Syst Ser B 13:537–557MathSciNetCrossRefMATH Apreutesei N, Bessonov N, Volpert V, Vougalter V (2010) Spatial structures and generalized travelling waves for an integro-differential equation. Discrete Contin Dyn Syst Ser B 13:537–557MathSciNetCrossRefMATH
2.
Zurück zum Zitat Shivanian E (2013) Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics. Eng Anal Bound Elem 37:1693–1702MathSciNetCrossRefMATH Shivanian E (2013) Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics. Eng Anal Bound Elem 37:1693–1702MathSciNetCrossRefMATH
3.
Zurück zum Zitat Fakhar-Izadi F, Dehghan M (2013) An efficient pseudo-spectral Legendre–Galerkin method for solving a nonlinear partial integro-differential equation arising in population dynamics. Math Methods Appl Sci 36(12):1485–1511MathSciNetCrossRefMATH Fakhar-Izadi F, Dehghan M (2013) An efficient pseudo-spectral Legendre–Galerkin method for solving a nonlinear partial integro-differential equation arising in population dynamics. Math Methods Appl Sci 36(12):1485–1511MathSciNetCrossRefMATH
4.
Zurück zum Zitat Ǵenieys S, Volpert V, Auger P (2006) Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Math Model Nat Phenom 1:65–82MathSciNetMATH Ǵenieys S, Volpert V, Auger P (2006) Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Math Model Nat Phenom 1:65–82MathSciNetMATH
6.
Zurück zum Zitat Britton NF (1990) Spatial structures and periodic travelling waves in an integro-differential reaction–diffusion population model. SIAM J Appl Math 50:1663–1688MathSciNetCrossRefMATH Britton NF (1990) Spatial structures and periodic travelling waves in an integro-differential reaction–diffusion population model. SIAM J Appl Math 50:1663–1688MathSciNetCrossRefMATH
7.
Zurück zum Zitat Al-Khaled K (2001) Numerical study of Fisher’s reaction–diffusion equation by the sinc collocation method. J Comput Appl Math 137:245–255MathSciNetCrossRefMATH Al-Khaled K (2001) Numerical study of Fisher’s reaction–diffusion equation by the sinc collocation method. J Comput Appl Math 137:245–255MathSciNetCrossRefMATH
8.
Zurück zum Zitat Branco JR, Ferrèira JA, de Oliveira P (2007) Numerical methods for the generalized Fisher–Kolmogorov–Piskunov equation. Appl Numer Math 57:89–102MathSciNetCrossRefMATH Branco JR, Ferrèira JA, de Oliveira P (2007) Numerical methods for the generalized Fisher–Kolmogorov–Piskunov equation. Appl Numer Math 57:89–102MathSciNetCrossRefMATH
9.
Zurück zum Zitat Carey GF, Shen Y (1995) Least-squares fnite element approximation of Fisher’s reaction–diffusion equation. Numer Methods Partial Differ Equ 11:175–186MathSciNetCrossRefMATH Carey GF, Shen Y (1995) Least-squares fnite element approximation of Fisher’s reaction–diffusion equation. Numer Methods Partial Differ Equ 11:175–186MathSciNetCrossRefMATH
10.
Zurück zum Zitat Daǧ I, Şahin A, Korkmaz A (2010) Numerical investigation of the solution of Fisher’s equation via the B-spline Galerkin method. Numer Methods Partial Differ Equ 26:1483–1503MATH Daǧ I, Şahin A, Korkmaz A (2010) Numerical investigation of the solution of Fisher’s equation via the B-spline Galerkin method. Numer Methods Partial Differ Equ 26:1483–1503MATH
11.
12.
Zurück zum Zitat Khuri SA, Sayfy A (2010) A numerical approach for solving an extended Fisher–Kolomogrov–Petrovskii–Piskunov equation. J Comput Appl Math 233:2081–2089MathSciNetCrossRefMATH Khuri SA, Sayfy A (2010) A numerical approach for solving an extended Fisher–Kolomogrov–Petrovskii–Piskunov equation. J Comput Appl Math 233:2081–2089MathSciNetCrossRefMATH
13.
15.
Zurück zum Zitat Perthame B, Ǵenieys S (2007) Concentration in the nonlocal fisher equation: the Hamilton-Jacobi limit. Math Model Nat Phenom 4:135–151MathSciNetCrossRefMATH Perthame B, Ǵenieys S (2007) Concentration in the nonlocal fisher equation: the Hamilton-Jacobi limit. Math Model Nat Phenom 4:135–151MathSciNetCrossRefMATH
16.
Zurück zum Zitat Liu G, Gu Y (2005) An introduction to meshfree methods and their programing. Springer, Berlin Liu G, Gu Y (2005) An introduction to meshfree methods and their programing. Springer, Berlin
18.
Zurück zum Zitat Belytschko T, Lu YY, Gu L (1995) Element free Galerkin methods for static and dynamic fracture. Int J Solids Struct 32:2547–2570CrossRefMATH Belytschko T, Lu YY, Gu L (1995) Element free Galerkin methods for static and dynamic fracture. Int J Solids Struct 32:2547–2570CrossRefMATH
19.
Zurück zum Zitat Dehghan M, Ghesmati A (2010) Combination of meshless local weak and strong (mlws) forms to solve the two dimensional hyperbolic telegraph equation. Eng Anal Bound Elem 34(4):324–336MathSciNetCrossRefMATH Dehghan M, Ghesmati A (2010) Combination of meshless local weak and strong (mlws) forms to solve the two dimensional hyperbolic telegraph equation. Eng Anal Bound Elem 34(4):324–336MathSciNetCrossRefMATH
20.
Zurück zum Zitat Kansa E (1990) Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates. Comput Math Appl 19(8–9):127–145MathSciNetCrossRefMATH Kansa E (1990) Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates. Comput Math Appl 19(8–9):127–145MathSciNetCrossRefMATH
21.
Zurück zum Zitat Dehghan M, Shokri A (2008) A numerical method for solution of the twodimensional sine-Gordon equation using the radial basis functions. Math Comput Simul 79:700–715MathSciNetCrossRefMATH Dehghan M, Shokri A (2008) A numerical method for solution of the twodimensional sine-Gordon equation using the radial basis functions. Math Comput Simul 79:700–715MathSciNetCrossRefMATH
22.
Zurück zum Zitat Pan R, Skala V (2011) A two-level approach to implicit surface modeling with compactly supported radial basis functions. Eng Comput 27(3):299–307CrossRef Pan R, Skala V (2011) A two-level approach to implicit surface modeling with compactly supported radial basis functions. Eng Comput 27(3):299–307CrossRef
23.
Zurück zum Zitat Dehghan M, Shokri A (2009) Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions. J Comput Appl Math 230(2):400–410MathSciNetCrossRefMATH Dehghan M, Shokri A (2009) Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions. J Comput Appl Math 230(2):400–410MathSciNetCrossRefMATH
24.
Zurück zum Zitat Aslefallah M, Shivanian E (2015) Nonlinear fractional integro-differential reaction–diffusion equation via radial basis functions. Eur Phys J Plus 130(47):1–9 Aslefallah M, Shivanian E (2015) Nonlinear fractional integro-differential reaction–diffusion equation via radial basis functions. Eur Phys J Plus 130(47):1–9
25.
Zurück zum Zitat Shivanian E (2015) A meshless method based on radial basis and spline interpolation for 2-D and 3-D inhomogeneous biharmonic BVPs. Zeitschrift für Naturforschung A 70(8):673–682CrossRef Shivanian E (2015) A meshless method based on radial basis and spline interpolation for 2-D and 3-D inhomogeneous biharmonic BVPs. Zeitschrift für Naturforschung A 70(8):673–682CrossRef
26.
Zurück zum Zitat Ling L, Opfer R, Schaback R (2006) Results on meshless collocation techniques. Eng Anal Bound Elem 30(4):247–253CrossRefMATH Ling L, Opfer R, Schaback R (2006) Results on meshless collocation techniques. Eng Anal Bound Elem 30(4):247–253CrossRefMATH
27.
Zurück zum Zitat Ling L, Schaback R (2008) Stable and convergent unsymmetric meshless collocation methods. SIAM J Numer Anal 46(3):1097–1115MathSciNetCrossRefMATH Ling L, Schaback R (2008) Stable and convergent unsymmetric meshless collocation methods. SIAM J Numer Anal 46(3):1097–1115MathSciNetCrossRefMATH
28.
Zurück zum Zitat Libre N, Emdadi A, Kansa E, Shekarchi M, Rahimian M (2008) A fast adaptive wavelet scheme in RBF collocation for nearly singular potential PDEs. CMES-Comput Model Eng Sci 38(3):263–284MathSciNetMATH Libre N, Emdadi A, Kansa E, Shekarchi M, Rahimian M (2008) A fast adaptive wavelet scheme in RBF collocation for nearly singular potential PDEs. CMES-Comput Model Eng Sci 38(3):263–284MathSciNetMATH
29.
Zurück zum Zitat Libre N, Emdadi A, Kansa E, Shekarchi M, Rahimian M (2009) A multiresolution prewavelet-based adaptive refinement scheme for RBF approximations of nearly singular problems. Eng Anal Bound Elem 33(7):901–914MathSciNetCrossRefMATH Libre N, Emdadi A, Kansa E, Shekarchi M, Rahimian M (2009) A multiresolution prewavelet-based adaptive refinement scheme for RBF approximations of nearly singular problems. Eng Anal Bound Elem 33(7):901–914MathSciNetCrossRefMATH
30.
Zurück zum Zitat Fakhar-Izadi F, Dehghan M (2014) Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains. Comput Math Appl 67(10):1884–1904MathSciNetCrossRef Fakhar-Izadi F, Dehghan M (2014) Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains. Comput Math Appl 67(10):1884–1904MathSciNetCrossRef
31.
Zurück zum Zitat Fatahi H, Saberi-Nadjafi J, Shivanian E (2016) A new spectral meshless radial point interpolation (SMRPI) method for the two-dimensional fredholm integral equations on general domains with error analysis. J Comput Appl Math 294:196–209MathSciNetCrossRefMATH Fatahi H, Saberi-Nadjafi J, Shivanian E (2016) A new spectral meshless radial point interpolation (SMRPI) method for the two-dimensional fredholm integral equations on general domains with error analysis. J Comput Appl Math 294:196–209MathSciNetCrossRefMATH
32.
Zurück zum Zitat Shivanian E (2015) Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation. Math Methods Appl Sci. doi:10.1002/mma.3604 Shivanian E (2015) Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation. Math Methods Appl Sci. doi:10.​1002/​mma.​3604
33.
Zurück zum Zitat Atluri S, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117–127MathSciNetCrossRefMATH Atluri S, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117–127MathSciNetCrossRefMATH
34.
Zurück zum Zitat Atluri S, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput Model Simul Eng 3(3):187–196 Atluri S, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput Model Simul Eng 3(3):187–196
36.
Zurück zum Zitat Atluri S, Zhu T (2000) The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics. Comput Mech 25:169–179CrossRefMATH Atluri S, Zhu T (2000) The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics. Comput Mech 25:169–179CrossRefMATH
37.
Zurück zum Zitat Dehghan M, Mirzaei D (2008) The meshless local Petrov–Galerkin (MLPG) method for the generalized two-dimensional non-linear schrödinger equation. Eng Anal Bound Elem 32:747–756CrossRefMATH Dehghan M, Mirzaei D (2008) The meshless local Petrov–Galerkin (MLPG) method for the generalized two-dimensional non-linear schrödinger equation. Eng Anal Bound Elem 32:747–756CrossRefMATH
38.
Zurück zum Zitat Dehghan M, Mirzaei D (2009) Meshless local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity. Appl Numer Math 59:1043–1058MathSciNetCrossRefMATH Dehghan M, Mirzaei D (2009) Meshless local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity. Appl Numer Math 59:1043–1058MathSciNetCrossRefMATH
39.
Zurück zum Zitat Gu Y, Liu G (2001) A meshless local Petrov–Galerkin (MLPG) method for free and forced vibration analyses for solids. Comput Mech 27:188–198CrossRefMATH Gu Y, Liu G (2001) A meshless local Petrov–Galerkin (MLPG) method for free and forced vibration analyses for solids. Comput Mech 27:188–198CrossRefMATH
40.
Zurück zum Zitat Abbasbandy S, Shirzadi A (2010) A meshless method for two-dimensional diffusion equation with an integral condition. Eng Anal Bound Elem 34(12):1031–1037MathSciNetCrossRefMATH Abbasbandy S, Shirzadi A (2010) A meshless method for two-dimensional diffusion equation with an integral condition. Eng Anal Bound Elem 34(12):1031–1037MathSciNetCrossRefMATH
41.
Zurück zum Zitat Shivanian E (2015) Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation. Eng Anal Bound Elem 50:249–257MathSciNetCrossRef Shivanian E (2015) Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation. Eng Anal Bound Elem 50:249–257MathSciNetCrossRef
42.
Zurück zum Zitat Shivanian E, Abbasbandy S, Alhuthali MS, Alsulami HH (2015) Local integration of 2-D fractional telegraph equation via moving least squares approximation. Eng Anal Bound Elem 56:98–105MathSciNetCrossRef Shivanian E, Abbasbandy S, Alhuthali MS, Alsulami HH (2015) Local integration of 2-D fractional telegraph equation via moving least squares approximation. Eng Anal Bound Elem 56:98–105MathSciNetCrossRef
43.
Zurück zum Zitat Dehghan M, Salehi R (2014) A meshless local Petrov–Galerkin method for the time-dependent maxwell equations. J Comput Appl Math 268:93–110MathSciNetCrossRefMATH Dehghan M, Salehi R (2014) A meshless local Petrov–Galerkin method for the time-dependent maxwell equations. J Comput Appl Math 268:93–110MathSciNetCrossRefMATH
44.
Zurück zum Zitat Taleei A, Dehghan M (2014) Direct meshless local Petrov–Glerkin method for elliptic interface problems with applications in electrostatic and elastostatic. Comput Methods Appl Mech Eng 278:479–498MathSciNetCrossRef Taleei A, Dehghan M (2014) Direct meshless local Petrov–Glerkin method for elliptic interface problems with applications in electrostatic and elastostatic. Comput Methods Appl Mech Eng 278:479–498MathSciNetCrossRef
45.
Zurück zum Zitat Dehghan M, Abbaszadeh M, Mohebbi A (2014) Numerical solution of system of n-coupled nonlinear schrodinger equations via two variants of the meshless local Petrov–Galerkin (mlpg) method. Comput Model Eng Sci CMES 100(5):399–444MathSciNet Dehghan M, Abbaszadeh M, Mohebbi A (2014) Numerical solution of system of n-coupled nonlinear schrodinger equations via two variants of the meshless local Petrov–Galerkin (mlpg) method. Comput Model Eng Sci CMES 100(5):399–444MathSciNet
46.
47.
Zurück zum Zitat Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRefMATH Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRefMATH
48.
Zurück zum Zitat Bratsos A (2008) An improved numerical scheme for the sine-Gordon equation in 2+1 dimensions. Int J Numer Meth Eng 75:787–799MathSciNetCrossRefMATH Bratsos A (2008) An improved numerical scheme for the sine-Gordon equation in 2+1 dimensions. Int J Numer Meth Eng 75:787–799MathSciNetCrossRefMATH
49.
Zurück zum Zitat Clear P (1998) Modeling conned multi-material heat and mass flows using SPH. Appl Math Model 22:981–993CrossRef Clear P (1998) Modeling conned multi-material heat and mass flows using SPH. Appl Math Model 22:981–993CrossRef
51.
Zurück zum Zitat Mukherjee Y, Mukherjee S (1997) Boundary node method for potential problems. Int J Numer Methods Eng 40:797–815CrossRefMATH Mukherjee Y, Mukherjee S (1997) Boundary node method for potential problems. Int J Numer Methods Eng 40:797–815CrossRefMATH
52.
Zurück zum Zitat Melenk J, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289–314MathSciNetCrossRefMATH Melenk J, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289–314MathSciNetCrossRefMATH
54.
Zurück zum Zitat Gu Y, Liu G (2002) A boundary point interpolation method for stress analysis of solids. Comput Mech 28:47–54CrossRefMATH Gu Y, Liu G (2002) A boundary point interpolation method for stress analysis of solids. Comput Mech 28:47–54CrossRefMATH
55.
Zurück zum Zitat Gu Y, Liu G (2003) A boundary radial point interpolation method (BRPIM) for 2-d structural analyses. Struct Eng Mech 15:535–550CrossRef Gu Y, Liu G (2003) A boundary radial point interpolation method (BRPIM) for 2-d structural analyses. Struct Eng Mech 15:535–550CrossRef
56.
Zurück zum Zitat Liu G, Yan L, Wang J, Gu Y (2002) Point interpolation method based on local residual formulation using radial basis functions. Struct Eng Mech 14:713–732CrossRef Liu G, Yan L, Wang J, Gu Y (2002) Point interpolation method based on local residual formulation using radial basis functions. Struct Eng Mech 14:713–732CrossRef
57.
Zurück zum Zitat Liu G, Gu Y (2001) A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J Sound Vib 246(1):29–46CrossRef Liu G, Gu Y (2001) A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J Sound Vib 246(1):29–46CrossRef
58.
Zurück zum Zitat Dehghan M, Ghesmati A (2010) Numerical simulation of two-dimensional sine-gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput Phys Commun 181:772–786MathSciNetCrossRefMATH Dehghan M, Ghesmati A (2010) Numerical simulation of two-dimensional sine-gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput Phys Commun 181:772–786MathSciNetCrossRefMATH
59.
Zurück zum Zitat Shivanian E, Khodabandehlo H (2014) Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions. Eur Phys J Plus 129:241–251CrossRef Shivanian E, Khodabandehlo H (2014) Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions. Eur Phys J Plus 129:241–251CrossRef
60.
Zurück zum Zitat Hosseini V, Shivanian E, Chen W (2015) Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation. Eur Phys J Plus 130:33–54CrossRef Hosseini V, Shivanian E, Chen W (2015) Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation. Eur Phys J Plus 130:33–54CrossRef
61.
Zurück zum Zitat Shivanian E (2014) Analysis of meshless local and spectral meshless radial point interpolation (MLRPI and SMRPI) on 3-D nonlinear wave equations. Ocean Eng 89:173–188CrossRef Shivanian E (2014) Analysis of meshless local and spectral meshless radial point interpolation (MLRPI and SMRPI) on 3-D nonlinear wave equations. Ocean Eng 89:173–188CrossRef
62.
Zurück zum Zitat Shivanian E (2015) A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms. Eng Anal Bound Elem 54:1–12MathSciNetCrossRef Shivanian E (2015) A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms. Eng Anal Bound Elem 54:1–12MathSciNetCrossRef
63.
Zurück zum Zitat Shivanian E On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations. Int J Numer Methods Eng (in press). doi:10.1002/nme.4960 Shivanian E On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations. Int J Numer Methods Eng (in press). doi:10.​1002/​nme.​4960
64.
Zurück zum Zitat Abbasbandy SE (2015) The effects of MHD flow of third grade fluid by means of meshless local radial point interpolation (MLRPI). Int J Ind Math 7(1):1–11 Abbasbandy SE (2015) The effects of MHD flow of third grade fluid by means of meshless local radial point interpolation (MLRPI). Int J Ind Math 7(1):1–11
65.
Zurück zum Zitat Shivanian E, Rahimi A, Hosseini M (2015) Meshless local radial point interpolation to three-dimensional wave equation with neumann’s boundary conditions. Int J Comput Math. doi:10.1080/00207160.2015.1085032 Shivanian E, Rahimi A, Hosseini M (2015) Meshless local radial point interpolation to three-dimensional wave equation with neumann’s boundary conditions. Int J Comput Math. doi:10.​1080/​00207160.​2015.​1085032
66.
Zurück zum Zitat Shivanian E, Khodabandehlo HR (2015) Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem. Ain Shams Eng J. doi:10.1016/j.asej.2015.07.009 Shivanian E, Khodabandehlo HR (2015) Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem. Ain Shams Eng J. doi:10.​1016/​j.​asej.​2015.​07.​009
67.
Zurück zum Zitat Lei Z, Tianqi G, Ji Z, Shijun J, Qingzhou S, Ming H (2014) An adaptive moving total least squares method for curve fitting. Measurement 49:107–112CrossRef Lei Z, Tianqi G, Ji Z, Shijun J, Qingzhou S, Ming H (2014) An adaptive moving total least squares method for curve fitting. Measurement 49:107–112CrossRef
68.
Zurück zum Zitat Hu D, Long S, Liu K, Li G (2006) A modified meshless local Petrov–Galerkin method to elasticity problems in computer modeling and simulation. Eng Anal Bound Elem 30:399–404CrossRefMATH Hu D, Long S, Liu K, Li G (2006) A modified meshless local Petrov–Galerkin method to elasticity problems in computer modeling and simulation. Eng Anal Bound Elem 30:399–404CrossRefMATH
69.
Zurück zum Zitat Liu K, Long S, Li G (2006) A simple and less-costly meshless local Petrov–Galerkin (MLPG) method for the dynamic fracture problem. Eng Anal Bound Elem 30:72–76CrossRefMATH Liu K, Long S, Li G (2006) A simple and less-costly meshless local Petrov–Galerkin (MLPG) method for the dynamic fracture problem. Eng Anal Bound Elem 30:72–76CrossRefMATH
Metadaten
Titel
Local integration of population dynamics via moving least squares approximation
verfasst von
E. Shivanian
Publikationsdatum
01.04.2016
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2016
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-015-0424-z

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