Numerical Solution of The First-Order Evolution Equations by Radial Basis Function
الموضوعات : فصلنامه ریاضی
1 - Qazvin Branch, Islamic Azad University
الکلمات المفتاحية: Newton', s method, First-order evolution equations, Radial basis function, nonlinear equations,
ملخص المقالة :
In this work, we consider the nonlinear first-order evolution equations: $u_t=f(x,t,u,u_x,u_{xx})$ for $0<t<\infty$, 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.
