Solving the Nonlinear Poisson Equation on the Unit Disk
نویسنده
چکیده
We propose and analyze a numerical method for solving the nonlinear Poisson equation −Δu = f(·, u) on the unit disk with zero Dirichlet boundary conditions. The problem is reformulated as a nonlinear integral equation. We use a Galerkin method with polynomials as approximations. The speed of convergence is shown to be very rapid; and experimentally the maximum error is exponentially decreasing when it is regarded as a function of the degree of the approximating polynomial.
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