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Engineering with Computers
Erschienen in: Engineering with Computers 1/2021

28.06.2019 | Original Article

The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method

verfasst von: Pouria Assari, Fatemeh Asadi-Mehregan

Erschienen in: Engineering with Computers | Ausgabe 1/2021

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Abstract

The charged particle motion for certain configurations of oscillating magnetic fields can be simulated by a Volterra integro-differential equation of the second order with time-periodic coefficients. This paper investigates a simple and accurate scheme for computationally solving these types of integro-differential equations. To start the method, we first reduce the integro-differential equations to equivalent Volterra integral equations of the second kind. Subsequently, the solution of the mentioned Volterra integral equations is estimated by the collocation method based on the local multiquadrics formulated on scattered points. We also expand the proposed method to solve fractional integro-differential equations including non-integer order derivatives. Since the offered method does not need any mesh generations on the solution domain, it can be recognized as a meshless method. To demonstrate the reliability and efficiency of the new technique, several illustrative examples are given. Moreover, the numerical results confirm that the method developed in the current paper in comparison with the method based on the globally supported multiquadrics has much lesser volume computing.
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Literatur
1.
Dehghan M, Shakeri F (2008) Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method. Prog Electromagn Res 78:361–376
2.
Maleknejad K, Hadizadeh M, Attary M (2013) On the approximate solution of integro-differential equations arising in oscillating magnetic fields. Appl Math 58(5):595–607MathSciNetMATH
3.
Machado JM, Tsuchida M (2002) Solutions for a class of integro-differential equations with time periodic coefficients. Appl Math E-Notes 2:66–71MathSciNetMATH
4.
Wazwaz AM (2011) Linear and nonlinear integral equations: methods and applications. Springer, HeidelbergMATH
5.
Pathak M, Joshi P (2014) High order numerical solution of a Volterra integro-differential equation arising in oscillating magnetic fields using variational iteration method. Int J Adv Sci Tech 69:47–56
6.
Brunner H, Makroglou A, Miller RK (1997) Mixed interpolation collocation methods for first and second order Volterra integro-differential equations with periodic solution. Appl Numer Math 23(4):381–402MathSciNetMATH
7.
Li F, Yan T, Su L (2014) Solution of an integral-differential equation arising in oscillating magnetic fields using local polynomial regression. Adv Mech Eng 1–9:2014
8.
Khan Y, Ghasemi M, Vahdati S, Fardi M (2014) Legendre multi-wavelets to solve oscillating magnetic fields integro-differential equations. UPB Sci Bull Ser A 76(1):51–58MathSciNetMATH
9.
Parand K, Rad JA (2012) Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via collocation method based on radial basis functions. Appl Math Comput 218(9):5292–5309MathSciNetMATH
10.
Ghasemi M (2014) Numerical technique for integro-differential equations arising in oscillating magnetic fields. Iran J Sci Technol A 38(4):473–479MathSciNet
11.
Assari P (2018) The thin plate spline collocation method for solving integrodifferential equations arisen from the charged particle motion in oscillating magnetic fields. Eng Comput 34:1706–1726
12.
Assari P, Dehghan M (2018) Solving a class of nonlinear boundary integral equations based on the meshless local discrete Galerkin (MLDG) method. Mediterr J Math 15:1–21MATH
13.
Drozdov AD, Gil MI (1996) Stability of a linear integro-differential equation with periodic coefficients. Q Appl Math 54(4):609–624MathSciNetMATH
14.
Hardy RL (2006) Hardy, multiquadric equations of topography and other irregular surfaces. J Geophys Res 176(8):1905–1915
15.
Fu Z, Chen W, Chen CS (2014) Recent advances in radial basis function collocation methods. Springer, New YorkMATH
16.
Kansa EJ (1990) Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-I. Comput Math Appl 19:127–145MathSciNetMATH
17.
Kansa EJ (1990) Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-II. Comput Math Appl 19:147–161MathSciNetMATH
18.
Fu Z, Reutskiy S, Sun H, Ma J, Khan MA (2019) A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains. Appl Math Lett 94:105–111MathSciNetMATH
19.
Fu Z, Xi Q, Chen W, Cheng AH-D (2018) A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations. Comput Math Appl 76(4):760–773MathSciNetMATH
20.
Wendland H (2005) Scattered data approximation. Cambridge University Press, New YorkMATH
21.
Lee CK, Liu X, Fan SC (2003) Local multiquadric approximation for solving boundary value problems. Comput Mech 30(5–6):396–409MathSciNetMATH
22.
Sarler B, Vertnik R (2006) Meshfree explicit local radial basis function collocation method for diffusion problems. Comput Math Appl 51(8):1269–1282MathSciNetMATH
23.
Sarra SA (2012) A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains. Appl Math Comput 218(19):9853–9865MathSciNetMATH
24.
Vertnik R, Sarler B (2006) Meshless local radial basis function collocation method for convective–diffusive solid–liquid phase change problems. Int J Numer Methods Heat Fluid Flow 16(5):617–640MathSciNetMATH
25.
Kosec G, Sarler B (2013) Solution of a low prandtl number natural convection benchmark by a local meshless method. Int J Numer Methods Heat Fluid Flow 23(1):189–204MathSciNetMATH
26.
Mramor K, Vertnik R, Sarler B (2013) Simulation of natural convection influenced by magnetic field with explicit local radial basis function collocation method. CMES Comput Model Eng Sci 92(4):327–352MathSciNetMATH
27.
Hon Y, Sarler B, Yun D (2015) Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface. Eng Anal Bound Elem 57:2–8MathSciNetMATH
28.
Siraj-Ul-Islam, Vertnik R, Sarler B (2013) Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations. Appl Numer Math 67:136–151MathSciNetMATH
29.
Wang B (2015) A local meshless method based on moving least squares and local radial basis functions. Eng Anal Bound Elem 50:395–401MathSciNetMATH
30.
Siraj ul Islam, Sarler B, Vertnik R, Kosec G (2012) Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled burgers’ equations. Appl Math Model 36(3):1148–1160MathSciNetMATH
31.
Yun DF, Hon YC (2016) Improved localized radial basis function collocation method for multi-dimensional convection-dominated problems. Eng Anal Bound Elem 67:63–80MathSciNetMATH
32.
Shu C, Ding H, Yeo KS (2003) Local radial basis funcion-based differential quadrature method and its application to solve two-dimensional incompressible navier–stokes equations. Comput Methods Appl Mech Eng 192(7–8):941–954MATH
33.
Yao G, Sarler B, Chen CS (2011) A comparison of three explicit local meshless methods using radial basis functions. Eng Anal Bound Elem 35(3):600–609MathSciNetMATH
34.
Yao G, Duo J, Chen CS, Shen LH (2015) Implicit local radial basis function interpolations based on function values. Appl Math Comput 265:91–102MathSciNetMATH
35.
Dehghan M, Nikpour A (2013) Numerical solution of the system of second-order boundary value problems using the local radial basis functions based differential quadrature collocation method. Appl Math Model 37(18–19):8578–8599MathSciNetMATH
36.
Sun J, Yi H, Tan H (2016) Local radial basis function meshless scheme for vector radiative transfer in participating media with randomly oriented axisymmetric particles. Appl Opt 55(6):1232–1240
37.
Mavric B, Sarler B (2015) Local radial basis function collocation method for linear thermoelasticity in two dimensions. Int J Numer Methods Heat Fluid 25(6):1488–1510MathSciNetMATH
38.
Dehghan M, Abbaszadeh M (2017) The meshless local collocation method for solving multi-dimensional Cahn–Hilliard, swift-Hohenberg and phase field crystal equations. Eng Anal Bound Elem 78:49–64MathSciNetMATH
39.
40.
Assari P, Adibi H, Dehghan M (2013) A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis. J Comput Appl Math 239(1):72–92MathSciNetMATH
41.
Assari P, Dehghan M (2017) A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions. Eur Phys J Plus 132:1–23MATH
42.
Assari P, Dehghan M (2017) A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions. Appl Math Comput 315:424–444MathSciNetMATH
43.
Assari P, Adibi H, Dehghan M (2014) The numerical solution of weakly singular integral equations based on the meshless product integration (MPI) method with error analysis. Appl Numer Math 81:76–93MathSciNetMATH
44.
Mirzaei D, Dehghan M (2010) A meshless based method for solution of integral equations. Appl Numer Math 60(3):245–262MathSciNetMATH
45.
Dehghan M, Salehi R (2012) The numerical solution of the non-linear integro-differential equations based on the meshless method. J Comput Appl Math 236(9):2367–2377MathSciNetMATH
46.
Li X (2011) Meshless Galerkin algorithms for boundary integral equations with moving least square approximations. Appl Numer Math 61(12):1237–1256MathSciNetMATH
47.
Li X, Zhu J (2009) A meshless Galerkin method for stokes problems using boundary integral equations. Comput Methods Appl Mech Eng 198:2874–2885MathSciNetMATH
48.
Fu Z, Chen W, Ling L (2015) Method of approximate particular solutions for constant- and variable-order fractional diffusion models. Eng Anal Bound Elem 57:37–46MathSciNetMATH
49.
Fu Z, Chen W, Yang H (2013) Boundary particle method for laplace transformed time fractional diffusion equations. J Comput Phys 235:52–66MathSciNetMATH
50.
Arqub OA, Al-Smadi M, Shawagfeh N (2013) Solving Fredholm integro-differential equations using reproducing Kernel Hilbert space method. Appl Math Comput 219(17):8938–8948MathSciNetMATH
51.
Arqub OA, Al-Smadi M (2014) Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations. Appl Math Comput 243(15):911–922MathSciNetMATH
52.
Shawagfeh N, Arqub OA, Momani SM (2014) Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method. J Comput Anal Appl 16(4):750–762MathSciNetMATH
53.
Halliday D, Resnick R, Walker J (1997) Fundamentals of physics. Willey, HobokenMATH
54.
Harrington RF (2003) Introduction to electromagnetic engineering. Courier Corporation
55.
Sadiku MNO (2007) Elements of electromagnetics. Oxford University Press, Oxford
56.
Bojeldain AA (1991) On the numerical solving of nonlinear Volterra integro-differential equations. Ann Univ Sci Bp Sect Comput 11:105–125MathSciNetMATH
57.
Fu Z, Chen W, Wen P, Zhang C (2018) Singular boundary method for wave propagation analysis in periodic structures. J Sound Vib 425:170–188
58.
Fasshauer GE (2005) Meshfree methods. In Handbook of theoretical and computational nanotechnology, American Scientific Publishers
59.
Assari P, Asadi-Mehregan F (2019) Local multiquadric scheme for solving two-dimensional weakly singular Hammerstein integral equations. Int J Numer Model 32(1):1–23MATH
60.
Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge University Press, CambridgeMATH
61.
Quarteroni A, Sacco R, Saleri F (2008) Numerical analysis for electromagnetic integral equations. Artech House, BostonMATH
62.
Atkinson KE (1997) The numerical solution of integral equations of the second kind. Cambridge University Press, CambridgeMATH
63.
Zhang S, Lin Y, Rao M (2000) Numerical solutions for second-kind Volterra integral equations by Galerkin methods. Appl Math 45(1):19–39MathSciNetMATH
64.
Arqub OA, Maayah B (2018) Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator. Chaos Solitons Fractals 117:117–124MathSciNetMATH
65.
Arqub OA, Al-Smadi M (2018) Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painleve equations in Hilbert space. Chaos Solitons Fractals 117:161–167MathSciNetMATH
66.
Arqub OA, Maayah B (2018) Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions. Numer Methods Partial Differ Equ 34:1577–1597MathSciNetMATH
67.
Arqub OA (2018) Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space. Numer Methods Partial Differ Equ 34:1759–1780MathSciNetMATH
68.
Arqub OA (2019) Application of residual power series method for the solution of time-fractional Schrodinger equations in one-dimensional space. Fundam Inform 166:87–110MathSciNetMATH
69.
Kaneko H, Xu Y (1994) Gauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kind. Math Comput 62(206):739–753MathSciNetMATH
70.
Metadaten
Titel
The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method
verfasst von
Pouria Assari
Fatemeh Asadi-Mehregan
Publikationsdatum
28.06.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 1/2021
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00807-z

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