Best approximation and numerical methods in solution of differential equations

Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations

ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and pseudospectral methods) are based on p...

Numerical Solution of Differential Equations

Chapter I - Numerical Methods for the Solution of Differential Equations

where f(y, t) = [f1(y, t), .., fn(y, t)] ∈ R is a vector valued function commonly referred to as a vector field. Thus for every y ∈ R it yields a time dependent vector f(y, t) in R. The fundamental theorem of ODE tells us that the equation (1.1) has a unique solution both forward and backward in time when the value of y(t) is specified at a certain time say t0, so that y(t0) = y 0 is given. In ...

Numerical Methods for the Solution of Partial Differential Equations

Numerical Methods for the Solution of Differential Equations