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

In this work, we consider the nonlinear rst-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 rst-order evolution equations and also the method is implemented in four numerical examples. The results reveal that the technique is very ective and simple.