Abstract :

The primary objective of this research paper is to introduce a novel technique known as the double ARA transform (DARAT) for effectively solving a broad spectrum of problems, encompassing both linear and nonlinear scenarios. This study specifically explores the application of DARAT to address the regular and singular one-dimensional coupled Burgers’ equations. Significant enhancements have been made to the original ARA transform to improve its precision and accuracy in handling linear problems. Additionally, DARAT has been seamlessly integrated with the well-established Adomian decomposition technique, which is renowned for its efficacy in solving nonlinear issues. The effectiveness of our proposed method is demonstrated through its remarkable ability to solve partial differential equations (PDEs), with the results clearly illustrated through graphical representations and detailed tables. These outcomes affirm the method’s robustness in deriving accurate solutions for both regular and singular coupled Burgers’ equations.