Nonlinear Differential Equations in Physics Novel Methods for Findin
This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by us
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Nonlinear Differential Equations in Physics Novel Methods for Finding Solutions
Nonlinear Differential Equations in Physics
Santanu Saha Ray
Nonlinear Differential Equations in Physics Novel Methods for Finding Solutions
123
Santanu Saha Ray Department of Mathematics National Institute of Technology Rourkela Odisha, India
ISBN 978-981-15-1655-9 ISBN 978-981-15-1656-6 https://doi.org/10.1007/978-981-15-1656-6
(eBook)
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Preface
This book provides brief introduction to the fractional derivatives and preliminaries of local fractional calculus and presents an overview of wavelets in mathematical preliminaries. The need of the present work for the scientific and engineering community also has been discussed succinctly in the book. In Chap. 1, various analytical and numerical methods for solving partial and fractional differential equations have been discussed along with some numerical methods for solving stochastic point kinetics equations. In Chap. 2, the utilization of new approaches of decomposition method in getting solutions for partial and fractional differential equations has been discussed. In this regard, a modified decomposition method has been newly applied for solving coupled Klein–Gordon– Schrödinger equations. In Chap. 3, the generalized order operational matrix of Haar wavelet has been used for finding the numerical solution of Bagley–Torvik equation. Next, the solutions of the Haar wavelet method are compared with OHAM as well as with the exact solutions for the fractional Fisher-type equation. The generalized order operational matrix of the Haar wavelet has b
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