Week 04-05: One-step, linear multi-step, Runge-Kutta, and Extrapolation methods; convergence
The extrapolated modified midpoint method is an excellent method for achieving high- order results with a rather simple second-order algorithm. This method works well for both smoothly varying problems and non-smoothly varying problems. This lesson is devoted to One-step, linear multi-step, Runge-Kutta, and Extrapolation methods and their convergence.
J. D. Hoffman, Numerical Methods for Engineers and Scientists, second ed. (Marcel Dekker, Inc, New York,.Basel, (1992))
Page No.: 471-480
Course Material
- Week 01: Classification of linear/non-linear second orders ODEs. Discuss the types of boundary conditions
- Week 02-03: Theory and implementation of numerical methods for initial and boundary value problems in ordinary differential equations.
- Week 04-05: One-step, linear multi-step, Runge-Kutta, and Extrapolation methods; convergence
- Week 06-07: stability, B-spline collocation methods for numerical solution of initial and boundary values problems
- Week 08: B-spline for solving class of singular and non-singular problems
- Week 09: Mid Term Exam
- Week 10: B-spline for solving class of singular and non-singular problems
- Week 11-13: Trigonometric B-spline approach for solving second order system of linear/non-linear ODEs.
- Week 14-15: B-spline solution for nonlinear differential equation arising in general relativity
- Week 16-17: Bratu’s problem, Perturbation’s problem
- Week 18: Final Term Exam
- Chapters 11
- Department Mathematics
- Teacher
Dr. Muhammad Abbas
