Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm

Parabolic equations play an important role in chemical engineering, vibration theory, particle diffusion and heat conduction. Solutions of such equations are required to analyze and pre-dict changes in physical systems. Solutions of such equations require efficient and effective tech-niques to get reasonable accuracy in lesser time. For this purpose, current article proposes residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions. The proposed algorithm provides closed-form solutions without linearization, discretization or perturbation. For efficiency testing of the proposed methodology, initially it is implemented to homogeneous multidimensional parabolic models, and exact solutions are com-puted. In next stage of testing, proposed algorithm is enforced to three-dimensional non-homoge-neous fourth order parabolic equation, and closed form solutions are recovered. The obtained results indicate the validity and effectiveness of proposed methodology, hence proposed algorithm can be extended to more complex scenarios in engineering and sciences. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

Parabolic equations are widely used in various fields such as chemical engineering, vibration theory, particle diffusion, and heat conduction. This article proposes a residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions, which provides closed-form solutions without linearization or perturbation. The algorithm has been tested on homogeneous and non-homogeneous parabolic models, demonstrating its validity and effectiveness for complex scenarios in engineering and sciences.