A wavelet operational method for solving fractional partial differential equations numerically

Wu, Jiunn-Lin

doi:10.1016/j.amc.2009.03.066

Cited by 109 publications

(74 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…And the numerical solution of the above example using Chebyshev wavelet operational matrix will be similar to the Haar wavelet matrix given by [2], as below: …”

Section: Examplementioning

confidence: 99%

“…In this section we shall use the numerical approach given by [2] to find the numerical solution for the linear fractional partial differential equations but by the second kind Chebyshev wavelet the integration of…”

Section: The Approachmentioning

confidence: 99%

“…Jafari and Seifi [12] solved a system of nonlinear fractional partial differential equations using homotopy analysis method. Wu [2] derived a wavelet operational method to solve fractional partial differential equations numerically. Chen and Wu [8] used wavelet method to find the numerical solution for a class of fractional convection-diffusion equation with variable coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the same approach given in [2] will be used but with the use of Chebyshev wavelets method to solve the fractional order partial differential equations. Wavelet analysis as a new approach of mathematics is widely applied in signal analysis, image manipulation, and numerical analysis, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Other applications include electromagnetic, electrochemistry, arterial science, and the theory of ultra-slow processes and finance, [2].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Chebyshev Wavelets Method for Solving Partial Differential Equations of Fractional Order

Mohammed

Ameen

2017

JNUS

View full text Add to dashboard Cite

In this paper, we use the second kind Chebyshev wavelet operational matrix of fractional integration for solving fractional order linear partial differential equations.By using this method the fractional order partial differential equation is translated into Lyapunov type matrix equation and the computation effort become convenient. Two illustrative examples are provided to demonstrate the validity, simplicity and applicability of the numerical scheme based on the Chebyshev set of functions.

show abstract

“…And the numerical solution of the above example using Chebyshev wavelet operational matrix will be similar to the Haar wavelet matrix given by [2], as below: …”

Section: Examplementioning

confidence: 99%

Section: The Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Other applications include electromagnetic, electrochemistry, arterial science, and the theory of ultra-slow processes and finance, [2].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chebyshev Wavelets Method for Solving Partial Differential Equations of Fractional Order

Mohammed

Ameen

2017

JNUS

View full text Add to dashboard Cite

show abstract

An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities

Radwan

Elwakil

2011

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

Efficient sustainable algorithm for numerical solution of nonlinear delay Fredholm‐Volterra integral equations via Haar wavelet for dense sensor networks in emerging telecommunications

Amin

Nazir

García‐Magariño

2020

Trans Emerging Tel Tech

View full text Add to dashboard Cite

Emerging technologies such as cloud computing, integration of Internet of Things, data science, self-powered data centers, dense sensor network, artificial intelligence convergence, machine learning and deep learning, self-service IT for business users and others play an important role in daily life. Dense sensor networks (DSNs) can be useful in fields such as structured health monitoring and turbine blades monitoring. Given the high number of sensors and the required small size, these sensors usually have very low processing capabilities for fitting to the size restrictions and limiting the production costs of the whole DSN. In this context, algorithms need to be really efficient so the algorithms can be achieved. This article focuses on providing an efficient algorithm for solving integral equations that can be useful in common problems in for emerging telecommunications. More concretely, this article presents an efficient numerical scheme for solution of nonlinear delay Fredholm integral equations, nonlinear delay Volterra integral equations and nonlinear delay Fredholm Volterra integral equations which are based on the use of Haar wavelets. Maximum absolute errors and experimental rates of convergence are computed using different numbers of collocation points.Numerical examples are given to show the computational efficiency of the proposed method. The numerical results exhibit that the technique is efficient and effective. The proposed research work can be used in wireless sensor network, emerging technologies, hereditary's phenomena in physics and heat transfer problems, electron emission and X-rays radiography.

show abstract

A wavelet operational method for solving fractional partial differential equations numerically

Cited by 109 publications

References 14 publications

Chebyshev Wavelets Method for Solving Partial Differential Equations of Fractional Order

Chebyshev Wavelets Method for Solving Partial Differential Equations of Fractional Order

An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities

Efficient sustainable algorithm for numerical solution of nonlinear delay Fredholm‐Volterra integral equations via Haar wavelet for dense sensor networks in emerging telecommunications

Contact Info

Product

Resources

About