10.71932/

Numerical Solution of the First-Order Evolution Equations by Radial Basis Function

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  • Sara Hosseini1,
  1. Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran.

Published in Issue 13-07-2025

Copyright (c) 2025 Sara Hosseini (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Hosseini, S. (2025). Numerical Solution of the First-Order Evolution Equations by Radial Basis Function. International Journal of Mathematical Modelling & Computations, 8(01). https://doi.org/10.71932/
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Abstract

In this work, we consider the nonlinear first-order evolution equations: ut = f(x; t; u; ux; uxx) for 0 < t < 1, subject to initial condition u(x; 0) = g(x), where u is a function of x and t and f is a known analytic function. The purpose of this paper is to introduce the method of RBF to existing method in solving nonlinear first-order evolution equations and also the method is implemented in four numerical examples. The results reveal that the technique is very effective and simple. 

Keywords

  • First-order evolution equations,
  • Radial basis function,
  • Newton’s method,
  • Nonlinear equations
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