Название: Advanced Numerical Methods for Differential Equations: Applications in Science and Engineering
Автор: Harendra Singh, Jagdev Singh, Sunil Dutt Purohit
Издательство: CRC Press
Год: 2021
Страниц: 337
Язык: английский
Формат: pdf (true)
Размер: 45,4 MB

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models.

This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science.

The book consists of 11 chapters and organized as follows:

Chapter 1 presents the numerical approximation of the fractional diffusion equation with a reaction term and discusses the stability and convergence of our numerical discretization, in the context of fractional calculus. The investigations and analysis concern the fractional differential equation described by the Caputo generalized fractional time derivative. The existence and uniqueness of the solution of the fractional diffusion equation are also provided using classical Banach fixed theorem. Graphical representations of the solutions have been presented to illustrate the main results of the chapter.

Chapter 2 investigates the complex and mixed dark-bright travelling wave solutions of the generalized KP-BBM equation. The sine-Gordon expansion method is used to produce dynamical complex wave properties. A wave transform considered is to convert the problems into a simple ordinary differential equation, providing a strong mathematical tool for solving other nonlinear development equations arising in mathematical physics...

Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.