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

Subject Areas : International Journal of Mathematical Modelling & Computations

Sara Hosseini ¹ ( Qazvin Branch, Islamic Azad University )

Received: 2019-02-25 Accepted : 2019-03-11 Published : 2018-01-01

Keywords: Newton&#039, s method, ‎First-order evolution equations, ‎Radial basis‎ ‎function, nonlinear equations‎,

Abstract :

‎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.