Chapter Study

Bsc CSIT Semester 3 – Numerical Method – Unit 6: Solution of Partial Differential Equations (5 Hrs.)

Comprehensive questions and detailed answers for Unit 6: Solution of Partial Differential Equations (5 Hrs.). Perfect for exam preparation and concept clarity.

Questions

Marks

Back to All Chapters

What is differential equation? Differentiate between ODE and PDE with example.

MediumNumerical5 marks2081(TU Final)

Solve the Poisson equation:

\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = -64xy, \quad 0 \le x \le 1,\; 0 \le y \le 1

subject to the boundary conditions:

\begin{aligned} u(0, y) &= 0, \\ u(x, 0) &= 0, \\ u(1, y) &= 150, \\ u(x, 1) &= 150. \end{aligned}

The mesh size is given by:

h = \frac{1}{3}.

MediumNumerical5 marks2081(TU Final)

Solve the Poisson’s equation $\nabla^2 f = xy$ and $f = 2$ on boundary by assuming square domain $0 \le x \le 3, \quad 0 \le y \le 3$ and $h=1.$

MediumNumerical5 marks2080(TU Final)

Solve the Poisson’s equation $\nabla^2f=3x^2y$ over the square domain $0 ≤ x ≤ 3, 0 ≤ y ≤ 3$ with $f=0$ on the boundary and $h=1$ .

MediumNumerical5 marks2079(TU Final)

A plate of dimension $18\text{ cm} \times 18\text{ cm}$ is subjected to temperatures as follows:

\text{Left side } = 100^\circ C, \quad \text{Right side } = 200^\circ C,

\text{Upper side } = 50^\circ C, \quad \text{Lower side } = 150^\circ C.

If square grid length of $6\text{ cm} \times 6\text{ cm}$ is assumed, what will be the temperature at the interior nodes?

MediumNumerical5 marks2077(TU Final)

Consider a metallic plate of size $90\,\text{cm} \times 90\,\text{cm}$ . The two adjacent sides of the plate are maintained at a temperature of $100^\circ C$ and the remaining two adjacent sides are held at $200^\circ C$ . Calculate the steady-state temperature at interior points assuming a grid size of $30\,\text{cm} \times 30\,\text{cm}$ .

MediumNumerical5 marks2078(TU Final)

Showing 6 questions