OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 8 01 2025 07 13 Numerical Solution of the First-Order Evolution Equations by Radial Basis Function 10.71932/ EN Sara Hosseini Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran. Journal Article 2025 07 13 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.