What are the numerical schme to solve fractional order model?
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Numerical schemes to solve fractional order models include a modified implicit finite difference approximation with a Fourier series approach for stability and convergence analysis . Another approach is the iterative reproducing kernel algorithm, which optimizes approximate solutions based on the Gram-Schmidt process on Sobolev spaces and generates Fourier expansions with fast convergence rates . The use of stochastic solvers, such as the Levenberg-Marquardt backpropagation scheme with neural networks, has also been implemented to solve fractional order models . A nonlocal explicit finite-difference scheme has been proposed for the numerical solution of nonlinear ordinary differential equations with fractional variable orders . Additionally, spectral collocation matrix methods and quasilinearization methods with Schröder polynomials as basis functions have been used to solve fractional mathematical models .
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| Papers (4) | Insight |
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| The paper discusses the use of two numerical schemes to solve the fractional order model: the spectral collocation matrix method and the quasilinearization method with Schröder polynomials as basis functions. | |
| The paper proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order. | |
| The paper proposes a modified implicit finite difference approximation scheme to numerically solve the fractional order cable model (FCM). | |
18 Citations | The paper proposes a novel reproducing kernel algorithm to solve a coupled system of fractional differential equations with integral boundary conditions. |
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