Solve Dirichlet problem for Laplace's equation u_xx + u_yy = 0 numerically in a rectangle R = [0,L] x [0,L].
Solve the linear system using Gauss-Seidel.QyQ+SSJMRzYiJCIjNSEiIiIiIg==QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJnBsb3RzR0YlISIiNumber of nodes along each axisQyQ+SSJORzYiIiIkIiIiStep sizeQyQ+SSJoRzYiKiZJIkxHRiUiIiJJIk5HRiUhIiJGKA==Boundary values (in the order lower,upper,left,right)QyQ+SSRmXzBHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUiIz9GJUYlRiUiIiI=QyQ+SSRmX0xHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUiJCE9RiVGJUYlIiIiQyQ+SSRnXzBHNiJmKjYjSSJ5R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUiIyEpRiVGJUYlIiIiQyQ+SSRnX0xHNiJmKjYjSSJ5R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUiIiFGJUYlRiUiIiI=QyQ+SSJ1RzYiLUkmYXJyYXlHJSpwcm90ZWN0ZWRHNiQ7IiIhSSJOR0YlRioiIiI=Initialize the matrix uQyQ/KEkiaUc2IiIiISIiIkkiTkdGJUkldHJ1ZUclKnByb3RlY3RlZEdDJj4mSSJ1R0YlNiRGJEYmLUkkZl8wR0YlNiMqJkYkRidJImhHRiVGJz4mRi42JEYkRigtSSRmX0xHRiVGMj4mRi42JEYmRiQtSSRnXzBHRiVGMj4mRi42JEYoRiQtSSRnX0xHRiVGMiEiIg==QyQ/KEkiaUc2IiIiIkYmLCZJIk5HRiVGJiEiIkYmSSV0cnVlRyUqcHJvdGVjdGVkRz8oSSJqR0YlRiZGJkYnRio+JkkidUdGJTYkRiRGLSIiIUYmNumber of iterations in Gauss-SeidelQyQ+SShOdW1JdGVyRzYiIiM1IiIiSolve by Gauss-SeidelQyQ/KEkia0c2IiIiIkYmSShOdW1JdGVyR0YlSSV0cnVlRyUqcHJvdGVjdGVkRz8oSSJqR0YlRiZGJiwmSSJOR0YlRiYhIiJGJkYoPyhJImlHRiVGJkYmRixGKD4mSSJ1R0YlNiRGMEYrLComRjM2JCwmRjBGJkYuRiZGKyNGJiIiJSZGMzYkLCZGMEYmRiZGJkYrRjkmRjM2JEYwLCZGK0YmRi5GJkY5JkYzNiRGMCwmRitGJkYmRiZGOUYmPlot resultsQyQ+SSJBRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQsJkkiTkdGJSIiIkYuRi5GLEYuQyQ/KEkiaUc2IiIiIkYmLCZJIk5HRiVGJkYmRiZJJXRydWVHJSpwcm90ZWN0ZWRHPyhJImpHRiVGJkYmRidGKT4mSSJBR0YlNiRGJEYsLUkmZXZhbGZHRio2IyZJInVHRiU2JCwmRixGJiEiIkYmLChGKEYmRiZGJkYkRjhGJg==QyQtSSZwcmludEclKnByb3RlY3RlZEc2I0kiQUc2IiIiIg==QyQtSSttYXRyaXhwbG90RzYiNiZJIkFHRiUvSSVheGVzR0YlSSZib3hlZEdGJS9JK3Byb2plY3Rpb25HRiUkIiIqISIiL0krZ2xvc3NpbmVzc0dGJSIiIkYy