Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies

A computational approach with the aid of Linear Multistep Method (LMM) for numerical solution differential equations initial value problems or boundary conditions has appeared several times in literature due to its good accuracy and stability properties. The major objective this article is extend a multistep Partial Differential Equation (PDE) originating from fluid mechanics two-dimensional space conditions, as result importance utility models partial applications, particularly physical phenomena, such convection-diffusion models, flow problems. Thus, collocation formula, which based on orthogonal polynomials proposed. Ninth-order Collocation Formulas (NMCFs) were formulated through principle interpolation processes. theoretical analysis NMCFs reveals that they have algebraic order nine, are zero-stable, consistent, and, thus, convergent. implementation strategies comprehensively discussed. Some test presented evaluate efficacy applicability proposed formulas. Comparisons other methods also demonstrate new formulas’ productivity. Finally, figures illustrate behavior examples.