New exact and numerical solutions with their stability for Ito integro-differential equation via Riccati–Bernoulli sub-ODE method
Abdulghani Alharbi, M. B. Almatrafi
Abstract
This paper points out several exact travelling wave solutions for $(1+1) $-dimensional Ito integro-differential equation via the Riccati–Bernoulli sub-ODE approach. We also aim to develop a numerical solution of the respective equation using central finite difference formulas. The stability of the presented exact and numerical solutions is also deduced using the Hamiltonian system and Von Neumann's concept, respectively. Moreover, the numerical schemes are studied in terms of their accuracy. The relative error arising from executing the numerical method is exhibited. We compare our results with others published in some articles. The accomplished numerical solutions are successfully compared with the analytical ones. The used processes can be extended to solve more integrable problems as well as non-integrable ones.