Solve Laplace Equation : ∇²ϕ=0

About the Solver

This solver calculates solutions to the Laplace equation in the interior of arbitrary simple closed 2-D domain for specified Dirichlet boundary conditions.

Simply input X and Y coordinates and the corresponding boundary values occuring in-between these coordinates to get the solution.

Precautions

Input the X-coordinate, Y-coordinate, and Boundary value occuring in-between co-oridnates as a list in Counter-Clockwise Direction.

Do not input the first co-ordinate twice (at first and last) to close the boundary. Put it only at the start.

Applications

The Laplace equation is used in fields like physics and engineering for problems involving electric potential, fluid dynamics, and heat conduction.

If you use this solver in your project, make sure to reference the author or website name.

Results: Surface Plot

Interactive Surface Plot