Improved Block-Pulse Functions for Numerical Solution of Mixed Volterra-Fredholm Integral Equations

The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a linear system of algebraic equations through the use of IBPFs in addition to the operational matrix of integration. Typically, the classical alterations have enhanced the time taken by the computer program to solve the system of algebraic equations. The current modification works perfectly and has improved the efficiency over the regular block–pulse basis functions (BPF). Additionally, the paper handles the uniqueness plus the convergence theorems of the solution. Numerical examples have been presented to illustrate the efficiency as well as the accuracy of the method. Furthermore, tables and graphs are used to show and confirm how the method is highly efficient.