A Higher Order Global Approximation Method for Solving an Abel Integral Equation by Quadratic Splines.

摘要

In the present paper, a global approximation method is developed for obtaining higher accuracy results involving higher order splines with full continuity. The quadratic spline case is investigated in detail. The technique is to differentiate the original equation, and solve the differentiated equation by using a quadratic spline in C(1). The computational effort required is only marginally greater than that required for a linear spline solution of the original equation. Convergence is obtained not only for the approximate solution but also for its first two derivatives at each point in the interval of integration.