Akgul, Ali2024-12-242024-12-2420211937-16321937-1179https://doi.org/10.3934/dcdss.2020261https://hdl.handle.net/20.500.12604/8361We give a new implementation of the reproducing kernel method to investigate difference equations in this paper. We obtain the solutions in terms of convergent series. The method of obtaining the approximate solution in form of an algorithm is presented. We demonstrate some experiments to prove the accuracy of the technique.eninfo:eu-repo/semantics/openAccessHilbert spacesdifference equationreproducing kernel functionsArticle14720412053Q2WOS:000661878900003Q12-s2.0-8510918132210.3934/dcdss.2020261