Advanced Numerical and Semi-Analytical Methods for Differential Equations

Preface

Differential equations form the backbone of various physical systems occurring in a wide range of science and engineering disciplines viz. physics, chemistry, biology, economics, structural mechanics, control theory, circuit analysis, biomechanics, etc. Generally, these physical systems are modeled either using ordinary or partial differential equations (ODEs or PDEs). In order to know the behavior of the system, we need to investigate the solutions of the governing differential equations. The exact solution of differential equations may be obtained using well‐known classical methods. Generally, the physical systems occurring in nature comprise of complex phenomena for which computation of exact results may be quite challenging. In such cases, numerical or semi‐analytical methods may be preferred. In this regard, there exist a variety of standard books related to solution of ODEs and PDEs. But, the existing books are sometimes either method or subject specific. Few existing books deal with basic numerical methods for solving the ODEs and/or PDEs whereas some other books may be found related with semi‐analytical methods only. But, as per the authors' knowledge, books covering the basic concepts of the numerical as well as semi‐analytical methods to solve various types of ODEs and PDEs in a systematic manner are scarce. Another challenge is that of handling uncertainty when introduced in the model. Moreover, some books include complex example problems which may not be convincing ...