Based on the principle of maximum entropy and piecewise linear basis functions, a numerical method for approximating a nonnegative solution of Volterra integral equations is proposed. Then a discrete form of the maximum entropy method is given to reduce the cost. The error analysis and the convergence rate are provided. Numerical experimental results are consistent with the theoretical analysis of errors and the convergence rate.
"SOLVING LINEAR VOLTERRA INTEGRAL EQUATIONS WITH A PIECEWISE LINEAR MAXIMUM ENTROPY METHOD." J. Integral Equations Applications 35 (1) 119 - 129, Spring 2023. https://doi.org/10.1216/jie.2023.35.119