This paper presents a Legendre-Galerkin spectral method to compute the solution of a distributed optimal control problem (OCP) constrained by the biharmonic equation on regular and irregular domains. First, the optimality system is obtained by the …

For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge–Kutta methods and continuous-stage Runge–Kutta methods …

Robust fused lasso (RFlasso) estimation plays an important role in regression analysis because it can deal with variable selection problems more robust than fused lasso for the case containing non-Gaussian distribution outliers, especially when …

In this paper, a penalty difference finite element (PDFE) method is presented for the 3D steady Navier-Stokes equations by using the finite element space pair $$(P_1^b, P_1^b, P_1) \times P_1$$ ( P 1 b , P 1 b , P 1 ) × P 1 in the direction of (x …

We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find sparse polyadic decompositions with elements of bounded maximal value of matrix multiplication tensors. We use this method to obtain …

Radial basis function finite difference (RBF-FD) discretization has recently emerged as an alternative to classical finite difference or finite element discretization of (systems) of partial differential equations. In this paper, we focus on the …

In this paper, the multi-term time-space fractional diffusion equation with fractional boundary conditions is considered. The fractional derivative in space is approximated by the standard and shifted $$Gr\ddot{u}nwald-Letnikov$$ G r u ¨ n w a l d …

Regularization is a method for providing a stable approximate solution to ill-posed operator equations, and it involves the regularization parameter which plays an important role in the convergence of the method. In this article, we propose a …

We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an …

The golden ratio primal-dual algorithm (GRPDA) was proposed for solving the saddle point problems which are being widely used in a variety of areas. Compared to the popular primal-dual algorithm (PDA), GRPDA allows for larger stepsizes by …

In this manuscript, we consider the non-characteristic Cauchy problem, which is naturally a general form including inverse heat conduction problem and sideways parabolic equation. This problem is a severely ill-posed problem, that is, the solution …

To improve the computational efficiency, based on the generalized alternating direction method of multipliers (GADMM), we consider a class of accelerated method for solving multi-block nonconvex and nonsmooth optimization problems. First, we …

Based on the finite-difference method, the considered Riesz space-fractional diffusion equations result in a series of linear systems, whose coefficient matrices are composed of the identity matrix and the product of diagonal matrix and Toeplitz …

Backward differential formulae (BDF) are the basis of the highly efficient schemes for the numerical solution of stiff ordinary differential equations for decades. An alternative multistep scheme (RBDF) based on barycentric rational interpolation …

In this article, the Kawahara and modified Kawahara equations with dual-power law nonlinearities are solved based on the sine-cosine method and finite difference schemes. The fourth-order accurate difference scheme for the Kawahara equation and …

A dynamical system given by a diffeomorphism with a three-dimensional phase space may have a blender, which is a hyperbolic set $$\Lambda $$ Λ with, say, a one-dimensional stable invariant manifold that behaves like a surface. This means that the …

We extend the error bounds from Chen et al. (SIAM J. Matrix Anal. Appl 43(2):787–811, 2022) for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to …

In this work, we present a new WENO B-spline-based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the B-spline functions, that form a partition of unity, instead of the …

The authors of Kaur and Natesan 2023 [A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance, (Numerical Algorithms, 94, (2023) 1519–1549)] proposed a numerical scheme, which is based on a …

This paper proposes a family of weighted- $$\theta $$ θ high-order ADI schemes for sine-Gordon equations in high dimensions in combination with the discretization of a three-level linearized scheme in temporal direction and a classical compact …