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

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

Course Outline

  • 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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