Question 1
Given the values of u(x,y) on the boundary of the square in the figure. Evaluate the function u(x,y) satisfying the Laplace’s equation \({ \nabla }^{ 2 }u=0\) at the interior mesh points of this figure.
Use Jacobi’s iteration method

Question 2
Solve the equation \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ \partial { y }^{ 2 } } =0 \), for the square mesh with boundary values as shown in the figure.

Question 3
Solve the Laplace’s equation \({ u }_{ xx }+{ u }_{ yy }=0\) employing five point formula with the following boundary conditions.
Find initial approximation

Solving Laplace Equation using Finite Difference Method - Solved Problem - I

Written by Tessy C

Lecturer and Research Scholar in Mathematics.