Advanced Numerical Techniques (MT5213)

None

Computational Methods In Engineering Boundary Value Problems By T. Y. Na , (1979) Edition

Numerical Analysis by Richard L. Burden and J. Douglas Faires , 9th Edition Edition

Analysis of Numerical Methods by H. B. Keller and Eugene Issacson , 2nd Edition Edition

This course has been designed to enable the students to learn and apply some classical numerical techniques to solve boundary value problems. For linear problems, the main focus will be on the method of superposition, method of chasing and method of adjoint operator whereas for the nonlinear equations, shooting methods will be discussed. Students are expected to apply these techniques in the research work involving boundary value problems.

After studying this course the students should be able to:

• learn some standard techniques of solving linear boundary value problems
• learn the shooting method for finding the solution of nonlinear boundary value problems

• The idea of Taylor’s Theorem and its role in numerical analysis
• Taylor’s method for the solution of initial value problems
• Solution of second order linear boundary value problems by the method of superposition
• Solution of third order linear boundary value problems by the method of superposition
• Solution of the system of first order linear boundary value problems by the method of superposition
• Method of chasing for the solution of second order linear boundary value problems
• Method of chasing for solution of third order linear boundary value problems
• Solution of the system of first order linear boundary value problems by the method of adjoint operator
• Solution of second order linear boundary value problems by the method of adjoint operators
• Shooting method involving Newton’s approach for the solution of nonlinear boundary value problems
• Parallel Shooting method for the solution of nonlinear boundary value problems
• Quasi Linearization of nonlinear boundary value problem