M 506 Ordinary and Partial Differential Equations 3(3,0) SEMESTER 1427 - 1428
Initial and boundary value problems for ordinary differential equations. Numerical solutions. Elliptic, parabolic and hyperbolic partial differential equations. Initial and boundary value problems for second order partial differential equations. Numerical solutions.
Classification of DE, Methods for solving ODE
Power series solutions of DE, Bessel’s equation, Legendre’s equations. Orthogonal functions, Sturm-Liouville problems.
Numerical solutions of ODE, single step method: Euler, Range-Kutta methods. Milne’s and Adam- Moulton methods.
Classification of second order PDE, solution of by separation of variable BVP using Fourier series. BVP leading to Bessel functions, BVP leading to Legendre Functions.
Numerical solution of BVP, Shooting method, Finite difference method, Collocation method, Releigh – Ritz method and Finite Element method.
Numerical solution of Elliptic, Parabolic and Hyperbolic PDE.
LIBRARY REFERENCE 515.3’53
- D.G. Zill, Michael R. Cullen
Differential equations with boundary value problems, 6th Ed.
Fourier series and integral of boundary value problems.
- Tyn Myint-U
Partial differential equations of Mathematical Physics, 2nd Ed.
Allied Differential equations 3rd Ed.
5. C.F.Gerald and P.O. Wheathey
Applied Numerical Analysis, 5th Ed.
- Mary L. Boas
Mathematical Methods in Physical Sciences
- Donal W. Trim
Applied Differential Equations
8. G. Strphenson
An introduction to Partial Differential Equations for science students.
Partial Differential Equations
- P. Duchateau, D.Zachmann
Applied Partial Differential Equations