Laplace equation in one dimension

Please solve the Laplace equation in one dimension on a region bounded between
x ∈ [0, 1], with the boundary condition Φ(0) = 1, and Φ(1) = 2.

Actually line should pass through (0,1) making 45 degree with x,y-axis.

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To solve Laplace’s equation numerically, a PDE solver is needed. In this example taken from the ModelingToolkit docs , ModelingToolkit.jl was used for symbolic representation and DiffEqOperators.jl for finite difference method (FDM).

i want to solve it without any pde solver. i think it is easy problem.

who? you? us? Is this a homework problem? If so:


Laplace equations in 1d is not a PDE. Just an ODE with boundary conditions. And a very simple solution.


@zdenek_hurak You are right. The 1D Laplace equation is a special case with an easily solvable analytical solution (a blog by Slawomir Polanski).

@raman_kumar If you are indeed trying to solve your homework, this video of solving 1D advection and diffusion might give you some ideas.

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