What are the numerical scheme for solving FDEs?
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Numerical schemes for solving fractional differential equations (FDEs) include the non-polynomial spline function with the conformable conjugate gradient method . Another scheme is the implicit numerical scheme, which is an extension of the L1 numerical scheme and has an error estimate of O(h2) . The operational matrix method can also be used, which involves using shifted Legendre polynomials and a collocation scheme to obtain a good approximation for the solution . Additionally, an operator-based scheme can be employed, where the analytic solution is constructed using a generalized differential operator and an infinite power series . Finite difference schemes are also commonly used, particularly in the context of scale-resolving methods for turbulence, such as Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) .
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| Papers (5) | Insight |
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| The paper discusses various aspects of finite difference schemes for turbulence simulations, but it does not explicitly mention the specific numerical schemes used for solving FDEs. | |
13 Jun 2021 3 Citations | The numerical scheme for solving FDEs in the provided paper is an operator-based scheme that uses a generalized differential operator to construct an analytic solution in the form of an infinite power series. The approximate numerical solution is obtained by truncating the power series. |
| The paper proposes an operational matrix method using shifted Legendre polynomials to solve multiorder tempered fractional differential equations. | |
| The paper proposes an implicit numerical scheme for solving fractional-order systems of delay differential equations. The scheme is an extension of the L1 numerical scheme and has an error estimate of O(h^2), where h is the step size. | |
| The paper proposes using the trigonometric spline method with the conformable conjugate gradient method as a numerical scheme for solving fractional differential equations (FDEs). |
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