Abstract
The novelty of this paper is to propose a numerical method for solving ordinary differential equations of the first order that include both linear and nonlinear terms (ODEs). The method is constructed in two stages, which may be called predictor and corrector stages. The predictor stage uses the dependent variable’s first- and second-order derivative in the given differential equation. In literature, most predictor–corrector schemes utilize the first-order derivative of the dependent variable. The stability region of the method is found for linear scalar first-order ODEs. In addition, a mathematical model for boundary layer flow over the sheet is modified with electrical and magnetic effects. The model’s governing equations are expressed in partial differential equations (PDEs), and their corresponding dimensionless ODE form is solved with the proposed scheme. A shooting method is adopted to overcome the deficiency of the scheme for solving only first-order boundary value ODEs. An iterative approach is also considered because the proposed scheme combines explicit and implicit concepts. The method is also compared with an existing method, producing faster convergence than an existing one. The obtained results show that the velocity profile escalates by rising electric variables. The findings provided in this study can serve as a helpful guide for investigations into fluid flow in closed-off industrial settings in the future.
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