Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients
Mathematics and Natural Sciences
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.
Available at: https://aquila.usm.edu/fac_pubs/754