__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.

## CHAPTER 1

### Classification of DE, Methods for solving ODE

## CHAPTER 2

## Power series solutions of DE, Bessel’s equation, Legendre’s equations. Orthogonal functions, Sturm-Liouville problems.

## CHAPTER 3

Numerical solutions of ODE, single step method: Euler, Range-Kutta methods. Milne’s and Adam- Moulton methods.

## CHAPTER 4

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.

## CHAPTER 5

## Numerical solution of BVP, Shooting method, Finite difference method, Collocation method, Releigh – Ritz method and Finite Element method.

## CHAPTER 6

Numerical solution of Elliptic, Parabolic and Hyperbolic PDE.

#### REFERENCES

#### LIBRARY REFERENCE 515.3’53

__ __

**D.G. Zill, Michael R. Cullen**

Differential equations with boundary value problems, 6^{th} Ed.

**J.R.Hanna**

Fourier series and integral of boundary value problems.

**Tyn Myint-U**

Partial differential equations of Mathematical Physics, 2^{nd} Ed.

**M.R.Spiegel**

Allied Differential equations 3rd Ed.

5. C.F.Gerald and P.O. Wheathey

Applied Numerical Analysis, 5^{th} 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.

**W.E.William**

Partial Differential Equations

**P. Duchateau, D.Zachmann**

Applied Partial Differential Equations