Overview numerical solutions for nonlinear partial differential equations with applications
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Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The University of Dodoma
Abstract
This study is concerned with overview numerical solution for nonlinear partial differential equations. Since it is not easily to iterate the numerical scheme manually, C++ is used to encode the numerical scheme in order to find the numerical solution and Matlab is employed in drawing the figures.
Chapter one consists of Introduction of Nonlinear Partial Differential equations,
Literature Review, Classification of Partial Differential Equations, Examples of
PDEs, Boundary Conditions, Taylor Expansion, Solution of a Partial Differential Equations, Truncation Error, Research Objective, Signification of the Study and Study Limitation.
Chapter two contains Formulas of Finite Difference, Consistency, Stability and Convergence, Numerical scheme of Burgers' Equation, Sine Gordon Equation, Kortoweg-de Vries Equation, Gardner Equation and Fisher's Equation.
Chapter three contains numerical and graphical results obtained by explicit scheme. In this chapter various examples of Burgers' equations, Sine Gordon
Equation, Kortoweg-de Vries Equation, Gardner Equation and Fisher's Equation are discussed.
Chapter four deals with Discussion, Conclusion and Recommendations.
Description
Dissertations (MSc Mathematics)
Keywords
Numerical solutions, Nonlinear differential equations, Nonlinear equations, Nonlinear models, Partial differential equations, PDE
Citation
Ndushi, L. (2015). Overview numerical solutions for nonlinear partial differential equations with applications. Dodoma: The University of Dodoma