The second-order moving grid method for a singularly perturbed Fredholm equation with the integral initial value condition
In order to overcome the rapid change of the exact solution of the singularly perturbed Fredholm integro-differential equation in very thin initial layer,a numerical method with the second order uni-form convergence with respect to the perturbation parameter in the infinity norm is proposed.Such a definite problem with the integral initial condition is discretized by the exponentially fitted finite difference scheme,where the composite trapezoidal rule is applied into the integral term,with the basic function meth-od.Directly resulting from the local truncation error estimate and the stability analysis,the global truncation error estimate,whose corollary is the second order uniform convergence derived from the boundary estimate and the equal distribution principle,is conducted.The steps of the moving mesh method,whose main idea is to equally distribute the arc length computed by the monitor function selected by the concrete form of the global error estimate,are listed.Two examples illustrate our theorical analyses and demonstrate that the moving mesh is superior to both the Shishkin mesh and the Bakhvalov mesh.
singularly perturbedFredholm integral equationmoving meshuniform convergence
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