Highly Accurate Stable Difference Schemes for Integral Type Time-Nonlocal Problems for Parabolic Differential Equation

In this study, integral type time-nonlocal problems for parabolic equation are investigated. Approximate solutions are studied. Single-step, absolutely stable third- and fourth-order difference schemes are developed for the numerical solution of the considered problems. Absolute stability of these schemes is rigorously established through corresponding theorems. Numerical experiments are conducted to illustrate the high accuracy of the schemes. The test examples confirm both the precision and robustness of the proposed approaches. Additionally, essential conditions for their effective implementation are provided.