Polynomial spline collocation methods for the nonlinear basset equation

Abstract We discuss the application of a class of spline collocation methods to a first-order Volterra integro-differential equation arising in fluid dynamics. Since this equation possesses a weakly singular kernel its solutions, even for analytic data, are not smooth on the entire interval of integration. It is shown that while the use of uniform grids leads to poor convergence rates, high-order convergence is restored on suitably graded grids.

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