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Nonlinear differential equations in ...

Saha Ray, Santanu.

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Nonlinear differential equations in physics = novel methods for finding solutions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear differential equations in physics/ by Santanu Saha Ray.
Reminder of title:	novel methods for finding solutions /
Author:	Saha Ray, Santanu.
Published:	Singapore :Springer Singapore : : 2020.,
Description:	xxxi, 388 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Mathematical Preliminaries -- 2. New Approaches for Decomposition Method for the Solution of Differential Equations -- 3. Numerical Solution of Fractional Differential Equations by using New Wavelet Operational Matrix of General Order -- 4. Numerical Solutions of Riesz Fractional Partial Differential Equations -- 5. New Exact Solutions of Fractional Order Partial Differential Equations -- 6. An Investigation for New Double Periodic Solutions of Coupled Schrodinger-Boussinesq Equations -- 7. New Techniques for Fractional Reduced Differential Transform Method -- 7. A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations -- 9. Numerical Simulation of Stochastic Point Kinetic Equation in the Dynamical System of Nuclear Reactor.
Contained By:	Springer eBooks
Subject:	Nonlinear theories. -
Online resource:	https://doi.org/10.1007/978-981-15-1656-6
ISBN:	9789811516566

Nonlinear differential equations in physics = novel methods for finding solutions /
Saha Ray, Santanu.

Nonlinear differential equations in physicsnovel methods for finding solutions /[electronic resource] :by Santanu Saha Ray. - Singapore :Springer Singapore :2020. - xxxi, 388 p. :ill., digital ;24 cm.

1. Mathematical Preliminaries -- 2. New Approaches for Decomposition Method for the Solution of Differential Equations -- 3. Numerical Solution of Fractional Differential Equations by using New Wavelet Operational Matrix of General Order -- 4. Numerical Solutions of Riesz Fractional Partial Differential Equations -- 5. New Exact Solutions of Fractional Order Partial Differential Equations -- 6. An Investigation for New Double Periodic Solutions of Coupled Schrodinger-Boussinesq Equations -- 7. New Techniques for Fractional Reduced Differential Transform Method -- 7. A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations -- 9. Numerical Simulation of Stochastic Point Kinetic Equation in the Dynamical System of Nuclear Reactor.

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.

ISBN: 9789811516566

Standard No.: 10.1007/978-981-15-1656-6doiSubjects--Topical Terms:

524352
Nonlinear theories.

LC Class. No.: QC20.7.N6 / S243 2020

Dewey Class. No.: 530.15

Nonlinear differential equations in physics = novel methods for finding solutions /
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100 1 $a Saha Ray, Santanu. $3 3446473
245 1 0 $a Nonlinear differential equations in physics $h [electronic resource] : $b novel methods for finding solutions / $c by Santanu Saha Ray.
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300 $a xxxi, 388 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1. Mathematical Preliminaries -- 2. New Approaches for Decomposition Method for the Solution of Differential Equations -- 3. Numerical Solution of Fractional Differential Equations by using New Wavelet Operational Matrix of General Order -- 4. Numerical Solutions of Riesz Fractional Partial Differential Equations -- 5. New Exact Solutions of Fractional Order Partial Differential Equations -- 6. An Investigation for New Double Periodic Solutions of Coupled Schrodinger-Boussinesq Equations -- 7. New Techniques for Fractional Reduced Differential Transform Method -- 7. A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations -- 9. Numerical Simulation of Stochastic Point Kinetic Equation in the Dynamical System of Nuclear Reactor.
520 $a 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.
650 0 $a Nonlinear theories. $3 524352
650 1 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Fourier Analysis. $3 891095
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-981-15-1656-6
950 $a Mathematics and Statistics (Springer-11649)