Overview Numerical Solutions For Nonlinear Partial Differential Equations With Applications

ABSTRACT

This study is concerned with overview numerical solution for nonlinear partial

dierential equations. Since it is not easily to iterate the numerical scheme

manually, C++ is used to encode the numerical scheme in order to nd the

numerical solution and Matlab is employed in drawing the gures.

Chapter one consists of Introduction of Nonlinear Partial Dierential equations,

Literature Review, Classication of Partial Dierential Equations, Examples of

PDEs, Boundary Conditions, Taylor Expansion, Solution of a Partial

Dierential Equations, Truncation Error, Research Objective, Signication of

the Study and Study Limitation.

Chapter two contains Formulas of Finite Dierence, 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.

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