A. Numerical Solution of Ordinary Differential Equations

Numerical solution of first order ordinary differential equations: Piccard’s method Taylor series method, Euler and modified Euler method, Runge Kutta methods.

Multi-step methods: Predictor corrector methods

Systems of equations and higher order equations.

Linear Boundary value problems: Shooting methods, Finite Difference Methods

Convergence criteria, Errors and error propagation, Stiff equations.

Nonlinear Boundary Value Problems

B. Numerical Solution of Partial Differential Equations

Classification, Finite Difference representation

Parabolic PDE: Explicit and implicit schemes. Compatibility, Stability and Convergence

Elliptic PDE: Solution of Laplace/Poisson PDE ADI and SOR schemes,

Hyperbolic equations: Finite difference schemes, Method of characteristics

Particulars

Hours

Numerical solution of order Ordinary Differential Equations

Initial value problems: definition, existence of solution, need for numerical solutions, Finite difference equation, truncation error

1

Piccard’s method of successive approximation. Taylor series method, Euler and modified Euler method

Fox, L. Numerical Solution of Ordinary & Partial Differential Equation, Pergamon Press

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