A hybrid approximation method for solving Hutchinson’s equation

The hybrid function approximation method for solving Hutchinson’s equation which is a nonlinear delay partial differential equation, is investigated. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials based on Legendre–Gauss-type points are presented and are utilized to replace the system of nonlinear delay differential equations resulting from the application of Legendre pseudospectral method, by a system of nonlinear algebraic equations. The validity and applicability of the proposed method are demonstrated through two illustrative examples on Hutchinson’s equation.

► A hybrid approximation method for solving Hutchinson’s equation is presented. ► The method is based on hybrid of block-pulse and Lagrange interpolating polynomials. ► The Legendre-Gauss-Lobatto points are used to discretize the problem. ► This approach converts the problem to a system of nonlinear algebraic equations.