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

Abstract

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 predict changes in physical systems. Solutions of such equations require efficient and effective techniques 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 computed. In next stage of testing, proposed algorithm is enforced to three-dimensional non–homogeneous 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.

Keywords

• Partial differential equations
• Residual power series
• Parabolic equations
• Series solution