Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients
The method of approximate particular solutions is extended for solving initial-boundary-value problems for general parabolic partial differential equations (PDEs) with variable coefficients. The main idea is to reduce the parabolic PDEs into a series of elliptic PDEs and approximate the unknown solution by the closed-form particular solution using radial basis functions. Numerical experiments in two and three dimensions show that the proposed scheme is accurate and easy to implement.
Numerical Heat Transfer Part B-Fundamentals
(2010). Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients. Numerical Heat Transfer Part B-Fundamentals, 57(5), 333-347.
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