Suppose b(x) is a function of a variable x, and let Dxx represent the second derivative d^2x/dx^2. Then the differential equation
1+Dxx u = b
u = (1+Dxx)\b.
I can’t figure out how to do this with
Let’s first consider the simpler equation: Dxx u = b. This can be solved as:
using DiffEqOperators L = 2*pi nx = 100 dx = L/(nx+1) xpoints = range(dx, step=dx, length=nx) b = sin.(xpoints) Dxx = CenteredDifference(2, 2, dx, nx) bc = Dirichlet0BC(Float64) sol = (Dxx*bc)\b
Based on this I want to do something like
(1+Dzz*bc)\b. However I can’t see how to make this work. I’ve tried using
I from the
LinearAlgebra package, the identity matrix, and a
CenteredDifference of order zero, but all gave an error. Does anyone know what the solution is?