Numerical Solution of Partial Differential Equations: Course Outline (MAT-634)

• Parabolic Equations.
• Explicit finite difference approximation.
• Crank Nickelson implicit method.
• Derivative boundary condition.
• The local truncation error.
• Consistency and Stability.
• The necessary and sufficient condition for stability.
• Finite difference approximation in spherical polar co-ordinates.
• Hyperbolic Equations.
• Analytic solution of quasi-linear equations.
• Finite difference method on a rectangular mesh for first order equations.
• Reducion of first order partial differential equation to a system of first order ordinary differential equations.
• Second order quasi-linear hyperbolic equations.
• Finite difference method on a rectangular mesh for second order equation.
• Simultaneous first order equations and stability.
• Elliptic Equations.
• Finite difference in polar co-ordinates.
• Formulae for derivative near curved boundaries.
• Improvement of the accuracy of solution.
• Systematic iterative methods for large linear  systems.
• Jacobbi.
• Gauss and SOR methods.
• Necessary and sufficient condition for convergence of iterative methods.
• Methods for accelerating convergence.

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