American Journal of Computational Mathematics · 2014 · 16 citations · 3 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical IntegrationNumerical Methods For Differential EquationsNumerical StabilityDifferential Equation SolversLinear Initial Value ProblemsNumerical Methods For Initial Value ProblemsNumerical Solutions Of Ordinary Differential EquationsOrdinary Differential Equation SolversOrdinary Differential Equation SystemsStability Of Numerical SchemesTime-stepping Schemes
In this paper we derived a continuous linear multistep method (LMM) with step number k = 5 through collocation and interpolation techniques using power series as basis function for approximate solution. An order nine p-stable scheme is developed which was used to solve the third order initial value problems in ordinary differential equation without first reducing to a system of first order equations. Taylor’s series algorithm of the same order was developed to implement our method. The result obtained compared favourably with existing methods.
3