Abstract
Numerical solution of a two-dimensional nonlinear singularly perturbed elliptic partial differential equation ? Δu?=?f(x, u), 0?<?x, y?<?1, with Dirichlet boundary condition is discussed here. The modified Newton method of third-order convergence is employed to linearize the nonlinear problem in place of the standard Newton method. The finite-element method is used to find the solution of the nonlinear differential equation. Numerical results are provided to demonstrate the usefulness of the method.
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