Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method

Single-term Walsh series are developed to approximate the solutions of nonlinear Volterra-Hammerstein integral equations. Properties of single-term Walsh series are presented and are utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples

A high order method for numerical solution of time-fractional KdV equation by radial basis functions

Abstract A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319–333, 1993). By choosing the centers of radial basis functions as collocation points, in each time step a nonlinear system of algebraic equations is obtained. A fixed point predictor–corrector method for solving the system is introduced. The efficiency and accuracy of our method are demonstrated through several illustrative examples. By the examples, the experimental convergence order is approximately $$4-\alpha$$ 4-α , where $$\alpha$$ α is the order of time derivative

Solution of time-varying singular nonlinear systems by single-term Walsh series

A method for finding the solution of time-varying singular nonlinear systems by using single-term Walsh series is proposed. The properties of single-term Walsh series are given and are utilized to find the solution of time-varying singular nonlinear systems

Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method

Single-term Walsh series are developed to approximate the solutions of nonlinear Volterra-Hammerstein integral equations. Properties of single-term Walsh series are presented and are utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.</p