Chapter Study

BCA Semester 4 – Numerical Methods – Unit 6: Solution of Partial Differential Equations (5Hrs.)

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

6

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30

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1

Solve the Poisson equation

\quad \quad ∇^2f=2x^2y^2

over the square domain $0≤x≤3,0≤y≤3$ with f=0 on the boundary and $h=1$ .

MediumTHEORY5 marks2021(TU FOHSS Final)

2

Write a short note on (Any Two):
$\quad$ a) Types of Errors
$\quad$ b) Convergent Methods
$\quad$ c) PDE

MediumTHEORY5 marks2021(TU FOHSS Final)

3

Solve the Poisson equation

\begin{aligned} \Delta^2 f &= 2x^2 y^2 \end{aligned}

over the square domain $0≤x≤3and0≤y≤3$ with $f=0$ on the boundary and $h=1$ .

MediumTHEORY5 marks2022(TU FOHSS Final)

4

Solve for the steady state temperatures in a rectangular plate of 8cm x 10cm, if one 10cm side is held at 50°C, and the other 10cm side is held at 30°C and other two sides are held at 10°C. Assume grids of size 2cm x 2cm.

MediumTHEORY5 marks2023(TU FOHSS Final)

5

Write a short note on (Any Two):
$\quad$ a) Partial Differential Equations
$\quad$ b) Linear Interpretation
$\quad$ c) Boundary value problems

MediumTHEORY5 marks2023(TU FOHSS Final)

6

Solve the laplace equation $Uxx + Uyy = 0$ for the following square mesh with the boundary values.

MediumTHEORY5 marks2024(TU FOHSS Final)

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Sample Questions

Solve the Poisson equation \[\quad \quad ∇^2f=2x^2y^2\] over the square domain \(0≤x≤3,0≤y≤3\) with f=0 on the boundary and \(h=1\).

Marks: 5Chapter: Unit 6: Solution of Partial Differential Equations (5Hrs.)

Write a short note on (Any Two):\ \(\quad \)a) Types of Errors\ \(\quad \)b) Convergent Methods\ \(\quad \)c) PDE

Marks: 5Chapter: Unit 6: Solution of Partial Differential Equations (5Hrs.)

Solve the Poisson equation \[ \begin{aligned} \Delta^2 f &= 2x^2 y^2 \end{aligned} \] over the square domain \(0≤x≤3and0≤y≤3\) with \(f=0\) on the boundary and \(h=1\).

Marks: 5Chapter: Unit 6: Solution of Partial Differential Equations (5Hrs.)

Solve for the steady state temperatures in a rectangular plate of 8cm x 10cm, if one 10cm side is held at 50°C, and the other 10cm side is held at 30°C and other two sides are held at 10°C. Assume gri

Marks: 5Chapter: Unit 6: Solution of Partial Differential Equations (5Hrs.)

Write a short note on (Any Two):\ \(\quad\) a) Partial Differential Equations\ \(\quad\) b) Linear Interpretation\ \(\quad\) c) Boundary value problems

Marks: 5Chapter: Unit 6: Solution of Partial Differential Equations (5Hrs.)

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