In the present paper, we introduce a non-polynomial
quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed
boundary value problems occur frequently in many areas of applied sciences such
as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion processes, hydrodynamics, aerodynamics, etc. These
problems have various important applications in fluid dynamics. The procedure
involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the
methodis analysed by the Von-Neumann
stability analysis. The developed method is tested with an illustrated
example, and the results are compared with other methods from the literature,
which shows the applicability and feasibility
of
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