Alexandria Engineering Journal · 2020 · 80 citations · 56 references
Natural SciencesComputational EngineeringMathematicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical IntegrationNumerical Methods For Differential EquationsDifferential Equation SolversFractional Differential EquationsNonlinear Differential-algebraic EquationsNumerical Solutions Of Partial Differential EquationsSecond-order Differential EquationsTruncation ErrorWavelet Analysis
This manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to various systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the efficiency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense.
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Variable Order and Distributed Order Fractional Operators
Carl F. Lorenzo, Tom T. Hartley · Nonlinear Dynamics · 2002 · 866 citations