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Approximate Solution Of Fractional Integro-Differential Equations By Taylor Expansion Method, Li Huang
Approximate Solution Of Fractional Integro-Differential Equations By Taylor Expansion Method, Li Huang
Li Huang
In this paper, Taylor expansion approach is presented for solving (approximately) a class of inear fractional integro-differential equations including those of Fredholm and of Volterra types. By means of themth-order Taylor expansion of the unknown function at an arbitrary point, the linear fractional integro-differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions. This method gives a simple and closed form solution for a linear fractional integro-differential equation. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.
Approximate Solution Of Abel Integral Equation, Li Huang
Approximate Solution Of Abel Integral Equation, Li Huang
Li Huang
This paper presents a new, stable, approximate inversion of Abel integral equation. By using the Taylor expansion of the unknown function, Abel equation is approximately transformed to a system of linear equations for the unknown function together with its derivatives. A desired solution can be determined by solving the resulting system according to Cramer’s rule. This method gives a simple and closed form of approximate Abel inversion, which can be performed by symbolic computation. The nth-order approximation is exact for a polynomial of degree up to n. Abel integral equation is approximately expressed in terms of integrals of input data; …
A New Abel Inversion By Means Of The Integrals Of An Input Function With Noise, Li Huang
A New Abel Inversion By Means Of The Integrals Of An Input Function With Noise, Li Huang
Li Huang
Abel’s integral equations arise inmany areas of natural science and engineering, particularly in plasma diagnostics. This paper proposes a new and effective approximation of the inversion of Abel transform. This algorithm can be simply implemented by symbolic computation, and moreover an nth-order approximation reduces to the exact solution when it is a polynomial in r2 of degree less than or equal to n. Approximate Abel inversion is expressed in terms of integrals of input measurement data; so the suggested approach is stable for experimental data with random noise. An error analysis of the approximation of Abel inversion is given. Finally, …