Related papers: Solution of Seventh Order Boundary Value Problems …
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems, named Hybrid Adaptive Dual Reciprocity Method (H-DRM). The…
In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem.
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving…
In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
Using critical point theory methods we undertake the existence and multiplicity of solutions for discrete anisotropic two-point boundary value problems.
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that classical symplectic…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…