A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

Khashan, M. Motawi; Amin, Rohul; Syam, Muhammed I.

doi:10.3390/math7060545

Cited by 20 publications

(9 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(13) gives the collocation points (CPs). Some of the recent work using HWC technique in literature can be seen in the references [28] , [29] , [30] , [31] , [32] , [33] , [34] .…”

Section: Haar Waveletmentioning

confidence: 99%

Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet

Amin

Shah

Asif

et al. 2020

Heliyon

Self Cite

View full text Add to dashboard Cite

In this article, a computational Haar wavelet collocation technique is developed for the solution of linear delay integral equations. These equations include delay Fredholm, Volterra and Volterra-Fredholm integral equations. First we transform the derived estimates for these equations. After that, we transform these estimates to a system of algebraic equations. Finally, we solve the obtained algebraic system by Gauss elimination technique. Numerical examples are taken from literature for checking the validity and convergence of the proposed technique. The maximum absolute and root mean square errors are compared with the exact solution. The convergence rate using distinct numbers of collocation points is also calculated, which is approximately equal to 2. All algorithms for the developed method are implemented in MATLAB (R2009b) software.

show abstract

“…(13) gives the collocation points (CPs). Some of the recent work using HWC technique in literature can be seen in the references [28] , [29] , [30] , [31] , [32] , [33] , [34] .…”

Section: Haar Waveletmentioning

confidence: 99%

Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet

Amin

Shah

Asif

et al. 2020

Heliyon

Self Cite

View full text Add to dashboard Cite

show abstract

“…The use of Haar wavelet have wide-ranging applications in scientific computing. The Haar Collocation Technique (HCT) is used for fractional Riccati type differential equations [30], Birthmark based identification [31], delay Fredholm-Volterra integral equations [32], delay integrodifferential equations [4], systems of fractional differential equations [33], and fractional integrodifferential equations [34] in recent literature. This article studies the solutions of second-order DDEs, that is, we develop numerical technique using Haar wavelet with constant delay.…”

Section: Introductionmentioning

confidence: 99%

Second‐Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

Xuan¹,

Amin

Zaman

et al. 2021

Wireless Communications and Mobile Computing

Self Cite

View full text Add to dashboard Cite

In this article, an efficient numerical approach for the solution of second-order delay differential equations to deal with the experimentation of the Internet of Industrial Things (IIoT) is presented. With the help of the Haar wavelet technique, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for various collocation points. The results show that the Haar wavelet method is an effective method for solving delay differential equations of second order. The convergence rate is also measured for various collocation points, which is almost equal to 2.

show abstract

“…Primarily, Haar wavelets convert a fractional differential equation into an algebraic system of equations with finite variables. The Haar wavelets approximation for tackling linear and nonlinear systems has been discussed in [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Green–Haar wavelets method for generalized fractional differential equations

et al. 2020

View full text Add to dashboard Cite

The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

show abstract

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

Cited by 20 publications

References 36 publications

Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet

Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet

Second‐Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

Green–Haar wavelets method for generalized fractional differential equations

Contact Info

Product

Resources

About