Numerical solutions of nonlinear 3‐dimensional Volterra integral‐differential equations with 3D‐block‐pulse functions

摘要

>This paper studies nonlinear 3‐dimensional Volterra integral‐differential equations, by implementing 3‐dimensional block‐pulse functions. First, we prove a theorem and corollary about sufficient condition for the minimum of mean square error under the block pulse coefficients and uniqueness of solution of the nonlinear Volterra integral‐differential equations. Then, we convert the main problem to a nonlinear system to the 3‐dimensional block‐pulse functions. In addition, illustrative examples are included to demonstrate the validity and applicability of the presented method.