A Walsh function method for a non-linear Volterra integral equation
The discontinuous Walsh functions which may be expressed in terms of the Haar functions, and can be obtained from the Rademacher system, form wavelet packets which are applied to a novel method for numerical solution of nonlinear Volterra integral equations. The presentation is clear and detailed: after an extended introduction and information on Walsh functions the solution method is explained carefully with conditions for the convergence of the method and a priori error estimates. The derived method is illustrated by means of two examples with analytical solutions: (i) a linear integral equation where the errors behave as expected, and (ii) a nonlinear integral equation which is solved also using the forward Euler method, besides the method in question; the numerical results are presented in detail (an obvious typo in (55)).
scientific article; zbMATH DE number 1925358
scientific article