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This research article is concerned with the solution of hydrodynamicstability based linear and nonlinear fourteenth order differentialproblem, which has great significance in applied physics, astrophysics,applied mathematics, engineering departments. The homotopy perturbationmethod (HPM) and optimal homotopy asymptotic method (OHAM)are applied for the solution of the existed problem. These semi analyticaltechniques are continuously evolved to solve diverse range of linear andnonlinear problems with effective approximate agents which is a rapid approachto the exact solutions. This approach is effectively proposed withdifferent numerical examples, which are taken from literature. Numericalresults are accomplished by phrase of convergent series solutions andapproach to the accurate solutions only by taking minimum steps. The numericalresults are exercised with exact solutions, cubic polynomial splinetechnique (CPST) and cubic non-polynomial spline technique (CNPST),excellent agreement has been observed. The observations suggested thatOHAM and HPM performed excellent in comparison to the CPST andCNPST in terms of solution, which demonstrated the effectiveness, potentialand validity of suggested schemes in reality and acquired resultsare of top-level perfection.