Masoud Saravi's Books

Nonlinear Ordinary Differential Equations

Analytical Approximation and Numerical Methods

By: Martin Hermann,Masoud Saravi

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Nonlinear Ordinary Differential Equations

Analytical Approximation and Numerical Methods

By: Martin Hermann,Masoud Saravi

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.

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Page Count

320

Publisher

Springer

Published Date

ISBN 10

813222812X

ISBN 13

9788132228127

A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

By: Martin Hermann,Masoud Saravi

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A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

By: Martin Hermann,Masoud Saravi

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

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Page Count

300

Publisher

Springer Science & Business

Published Date

ISBN 10

8132218353

ISBN 13

9788132218357

A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

By: Martin Hermann,Masoud Saravi

Write a review Read reviews Take a Quiz Solve Book Puzzle

A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

By: Martin Hermann,Masoud Saravi

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

300

Publisher

Springer Science & Business

Published Date

ISBN 10

8132218353

ISBN 13

9788132218357

Book's by Masoud Saravi

Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations

A First Course in Ordinary Differential Equations

A First Course in Ordinary Differential Equations

A First Course in Ordinary Differential Equations

A First Course in Ordinary Differential Equations

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