Book Review: Numerical methods for evolutionary differential equations

Numerical methods for evolutionary differential equations

Solutions to selected exercises and additional examples for my book Numerical Methods for Evolutionary Differential Equations

In this file I have collected solutions to selected exercises appearing in my book. Some of these solutions extend beyond what is strictly required in the question. Others leave details out. These solved exercises serve as additional examples for the text as well. It is seriously recommended that you try to solve the posed problems before taking a peak at the answers. This file represents work ...

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations

After revisiting some practical problems of numerical methods by playing with models introduced in Chapter 2, we will investigate the two most important properties of numerical algorithms—stability and accuracy. This is done most easily in the context of the simplest numerical method, i.e., the explicit Euler method (Section 5.2). The problem of solving stiff differential equations is addressed...

A Review of Numerical Methods for Nonlinear Partial Differential Equations

Numerical methods were first put into use as an effective tool for solving partial differential equations (PDEs) by John von Neumann in the mid1940s. In a 1949 letter von Neumann wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called ...