Abstract
We reduce solution of the Dirichlet problem (x∈D⊂Rm)Δu(x)+a(x)u(x)=f(x)in D,u=0on ∂Dto iterative solution of a simpler problemΔu=f(x)in D,u=0on ∂D,for which one can use either Fourier series or Green's function method. The method is suitable for numerical computations, particularly when one uses Newton's method for semilinear problemsΔu+g(x,u)=0in D,u=0on ∂D,.
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