MA20102: Numerical Solution Of Ordinary And Pde
| MA20102 | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Course name | Numerical Solution Of Ordinary And Pde | ||||||||||||||||||||||||||||
| Offered by | Mathematics | ||||||||||||||||||||||||||||
| Credits | 3 | ||||||||||||||||||||||||||||
| L-T-P | 3-0-0 | ||||||||||||||||||||||||||||
| Previous Year Grade Distribution | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
| Semester | Spring | ||||||||||||||||||||||||||||
Syllabus
Syllabus mentioned in ERP
Prerequisite: void Ordinary Differential Equations: Numerical solutions of IVP - Difference equations, stability, error and convergence analysis. Single step methods - Taylor series method, Euler method, Picardâs method of successive approximation, Runge Kutta Method. Multi step methods - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method. System of first order ODE, higher order IVPs. Numerical solutions of BVP - Linear BVP, finite difference methods, shooting methods, Newtonâs method for system of equations, stability, error and convergence analysis, non linear BVP, higher order BVP. Partial Differential Equations: Classification of PDEs, Finite difference approximations to partial derivatives, convergence and stability analysis. Explicit and Implicit schemes - Crank-Nicolson scheme, tri-diagonal system, Laplace equation using standard five point formula and diagonal five point formula. ADI scheme, hyperbolic equation, explicit scheme, method of characteristics. Solution of one dimensional heat conduction equation by Schmidt and Crank Nicolson methods. Solution of wave equation.
Concepts taught in class
Prerequisite: void Ordinary Differential Equations: Numerical solutions of IVP - Difference equations, stability, error and convergence analysis. Single step methods - Taylor series method, Euler method, Picardâs method of successive approximation, Runge Kutta Method. Multi step methods - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method. System of first order ODE, higher order IVPs. Numerical solutions of BVP - Linear BVP, finite difference methods, shooting methods, Newtonâs method for system of equations, stability, error and convergence analysis, non linear BVP, higher order BVP. Partial Differential Equations: Classification of PDEs, Finite difference approximations to partial derivatives, convergence and stability analysis. Explicit and Implicit schemes - Crank-Nicolson scheme, tri-diagonal system, Laplace equation using standard five point formula and diagonal five point formula. ADI scheme, hyperbolic equation, explicit scheme, method of characteristics. Solution of one dimensional heat conduction equation by Schmidt and Crank Nicolson methods. Solution of wave equation.
Student Opinion
| We learn many methods to find approximate solutions to differential equations with shocking accuracy.The material is very practical as can be directly used in many departmental subjects.The methods are very interesting can motivate the students to learn more about them.On other note,The course is tough and hectic and takes so much time to practise. |
How to Crack the Paper
| The course is tough compared to other mathematics subjects.The course has very less theory part but needs so much practice. Someone with less calculation speed and who has the habit of making calculation errors is going to suffer. However this can be avoided by practicing regularly.
The problems are almost the same every year but still one needs to learn everything.The best way to performance in this is to understand the concepts clearly and practice regularly. |
Classroom resources
Numerical Solutions to Differential Equations - MK Jain