scholarly journals On skewed grid point iterative method for solving 2D hyperbolic telegraph fractional differential equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ajmal Ali ◽  
Norhashidah Hj. Mohd. Ali
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Fractional Differential Equation ◽  
Grid Point ◽  
Fractional Differential

scholarly journals A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xiaomin Wang
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Numerical Integration ◽  
Fractional Differential Equation ◽  
Unknown Function ◽  
Nonlinear Fractional Differential Equation ◽  
Orthogonal Wavelets ◽  
Riccati Differential Equations ◽  
Fractional Differential ◽  
Approximate Scheme

A wavelet iterative method based on a numerical integration by using the Coiflets orthogonal wavelets for a nonlinear fractional differential equation is proposed. With the help of Laplace transform, the fractional differential equation was converted into equivalent integral equation of convolution type. By using the wavelet approximate scheme of a function, the undesired jump or wiggle phenomenon near the boundary points was avoided and the expansion constants in the approximation of arbitrary nonlinear term of the unknown function can be explicitly expressed in finite terms of the expansion ones of the approximation of the unknown function. Then a numerical integration method for the convolution is presented. As an example, an iterative method which can solve the singular nonlinear fractional Riccati equations is proposed. Numerical results are performed to show the efficiency of the method proposed.

scholarly journals Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andang Sunarto ◽  
Praveen Agarwal ◽  
Jumat Sulaiman ◽  
Jackel Vui Lung Chew ◽  
Elayaraja Aruchunan
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Iterative Method ◽  
Difference Scheme ◽  
Fractional Differential Equation ◽  
Relaxation Method ◽  
Mathematical Physics ◽  
One Dimensional ◽  
Fractional Differential ◽  
Preconditioned Iterative

AbstractThis paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to the time-fractional differential equation by applying the computational complexity reduction approach by the quarter-sweep technique. The finite-difference approximation equation will be formulated based on the Caputo’s time-fractional derivative and quarter-sweep central difference in space. The developed approximation equation generates a linear system on a large scale and has sparse coefficients. With the quarter-sweep technique and the preconditioned iterative method, computing the time-fractional differential equation solutions can be more efficient in terms of the number of iterations and computation time. The quarter-sweep computes a quarter of the total mesh points using the preconditioned iterative method while maintaining the solutions’ accuracy. A numerical example will demonstrate the efficiency of the proposed quarter-sweep preconditioned accelerated over-relaxation method against the half-sweep preconditioned accelerated over-relaxation, and the full-sweep preconditioned accelerated over-relaxation methods. The numerical finding showed that the quarter-sweep finite difference scheme and preconditioned accelerated over-relaxation method can serve as an efficient numerical method to solve fractional differential equations.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

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