A Modified Runge–Kutta and Compact Spatial Scheme for Darcy Forchheimer Prandtl–Eyring Fluid Flow Over a Riga Plate
Abstract
A modification of existing third order Runge-Kutta method, is proposed. The scheme is explicit, and its first stage consists of a nonstandard denominator, while the last two stages are the same as those of the Runge-Kutta method. For discretizing space-dependent terms, a compact, high-order scheme is employed. The proposed scheme with spatial discretization is employed to find the stability condition of the proposed scheme. The scheme is applied to a dimensionless model in the form of partial differential equations for the slip flow of a non-Newtonian fluid over a Riga plate with heat and mass transfer. Different types of graphs are obtained using the proposed scheme for velocity, temperature, and concentration profiles. Some of the results obtained by the proposed scheme are compared with those obtained by the numerical solution using the MATLAB PDEPE solver. The scheme is also compared with an existing third-order Runge-Kutta scheme, and it produces more accurate results than the existing scheme at specific time and space step sizes.
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References
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Copyright (c) 2026 Yasir Nawaz, Muhammad Shoaib Arif, Muavia Mansoor, Kamal Abodayeh
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