Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Stepwise stability for the heat equation with a nonlocal constraint
SIAM Journal on Numerical Analysis
Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions
Journal of Computational and Applied Mathematics - Special issue: positive solutions of nonlinear problems
Numerical solution of the heat equation with nonlocal boundary conditions
Journal of Computational and Applied Mathematics
Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions
Journal of Computational and Applied Mathematics
Stability in the numerical solution of the heat equation with nonlocal boundary conditions
Applied Numerical Mathematics
Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
Applied Numerical Mathematics
On the numerical solution of the heat conduction equations subject to nonlocal conditions
Applied Numerical Mathematics
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
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Nonlocal conditions arise in mathematical models of various physical, chemical or biological processes. Therefore, interest in developing computational techniques for the numerical solution of partial differential equations (PDEs) with various types of nonlocal conditions has been growing fast. We construct and analyse a weighted splitting finite-difference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the method. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme. We demonstrate that depending on the parameters of the finite-difference scheme and nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiments with several test problems are also presented and they validate theoretical results.