Application of a Hybrid of the Different Transform Method and Adomian Decomposition Method Algorithms to Solve the Troesch Problem

• Published in: Mathematics (Basel) Vol. 12; no. 23; p. 3858
• Main Authors: Pleszczyński, Mariusz, Kaczmarek, Konrad, Słota, Damian
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2024
• Subjects: Adomian decomposition method; Algorithms; Decomposition; differential equations; DTM; Integral equations; Methods; Ordinary differential equations; Partial differential equations; Polynomials; Task complexity; Troesch problem
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math12233858

The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decomposition Method (ADM). The combination of these two methods resulted in a continuous approximate solution to this problem and eliminated the problems that occur when trying to use each of these methods separately. The great advantages of the DTM method are the continuous form of the solution and the fact that it easy to implement error control. However, in too-complex tasks, this method becomes difficult to use. By using a hybrid of ADM and DTM, we obtain a relatively simple-to-implement method that retains the advantages of the DTM approach.