Nonlinear differential equations in physics : novel methods for finding solutions / Santanu Saha Ray.
2020
QC20.7.N6
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Title
Nonlinear differential equations in physics : novel methods for finding solutions / Santanu Saha Ray.
Author
Saha Ray, Santanu.
ISBN
9789811516566 (electronic book)
9811516561 (electronic book)
9811516553
9789811516559
9811516561 (electronic book)
9811516553
9789811516559
Publication Details
Singapore : Springer, 2020.
Language
English
Description
1 online resource
Call Number
QC20.7.N6
Dewey Decimal Classification
530.15
Summary
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 using Euler-Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers-Hopf equation, the (3+1)-dimensional time-fractional Khokhlov-Zabolotskaya-Kuznetsov equation, (3+1)-dimensional time-fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov equation, fractional (2+1)-dimensional Davey-Stewartson equation, and integrable Davey-Stewartson-type equation. Many of the methods discussed are analytical-numerical, namely the modified decomposition method, a new two-step Adomian decomposition method, new approach to the Adomian decomposition method, modified homotopy analysis method with Fourier transform, modified fractional reduced differential transform method (MFRDTM), coupled fractional reduced differential transform method (CFRDTM), optimal homotopy asymptotic method, first integral method, and a solution procedure based on Haar wavelets and the operational matrices with function approximation. The book proposes for the first time a generalized order operational matrix of Haar wavelets, as well as new techniques (MFRDTM and CFRDTM) for solving fractional differential equations. Numerical methods used to solve stochastic point kinetic equations, like the Wiener process, Euler-Maruyama, and order 1.5 strong Taylor methods, are also discussed.
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Includes bibliographical references.
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Print version: 9789811516559
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