Abstract and Applied Analysis · 2013 · 97 citations · 36 references
Natural SciencesComputational EngineeringPhysicsComputational Fluid DynamicsDifferential EquationsFluid DynamicsNonlinear DynamicsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsPerturbation MethodsPerturbation TheoryDifferential Equation SolversFractional Differential EquationsPerturbation Of Nonlinear Differential Equations
A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.
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J. W. Craggs · The Mathematical Gazette · 1973 · 4.2K citations
Homotopy perturbation technique
Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering · 1999 · 3.5K citations