Legendre wavelet method combined with the Gauss quadrature rule for numerical solution of fractional integro-differential equations

سال انتشار:

1401

نوع سند:

مقاله ژورنالی

زبان:

انگلیسی

مشاهده:

63

فایل این مقاله در 21 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:

شناسه ملی سند علمی:

JR_IJNAO-12-1_012

تاریخ نمایه سازی: 21 فروردین 1401

چکیده مقاله:

In this paper, we use a novel technique to solve the nonlinear fractional Volterra-Fredholm integro-differential equations (FVFIDEs). To this end, the Legendre wavelets are used in conjunction with the quadrature rule for converting the problem into a linear or nonlinear system of algebraic equations, which can be easily solved by applying mathematical programming techniques. Only a small number of Legendre wavelets are needed to obtain a satisfactory result. Better accuracies are also achieved within the method by increasing the number of polynomials. Furthermore, the existence and uniqueness of the solution are proved by preparing some theorems and lemmas. Also, error estimation and convergence analyses are given for the considered problem and the method. Moreover, some examples are presented and their results are compared to the results of Chebyshev wavelet, Nystro¨m, and Newton–Kantorovitch methods to show the capability and validity of this scheme. 

کلیدواژه ها:

Legendre wavelet ، Gaussian quadrature ، Operational matrix ، fractional Volterra-Fredholm integro-differential equations

نویسندگان

M.Riahi Beni
M. Riahi Beni

Department of Mathematics, Higher Education Complex of Saravan, Saravan, Iran.

مراجع و منابع این مقاله:

لیست زیر مراجع و منابع استفاده شده در این مقاله را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود مقاله لینک شده اند :
  • Abbasbandy, S., Hashemi, M., Hashim, I.On convergence of homotopy analysis ...
  • Alkan, S., Hatipoglu, V.F.Approximate solutions of Volterra-fredholm integro-differential equations of ...
  • Amin, R., Alshahrani, B., Mahmoud, M., Abdel-Aty, A.H., Shah, K., ...
  • Amin, R., Shah, K., Asif, M., Khan, I.A computational algorithm ...
  • Amin, R., Shah, K., Asif, M., Khan, I., Ullah, F.An ...
  • Bhrawy, A., Zaky, M., Van Gorder, R.A.A space-time Legendre spectraltau ...
  • Erfanian, M., Gachpazan, M., Beiglo, H.A new sequential approach for ...
  • Guner, O., Bekir, A.Exp-function method for nonlinear fractional differential equations, ...
  • Hamoud, A., Ghadle, K.The reliable modified of Laplace Adomian decomposition ...
  • Hashemi, M., Ashpazzadeh, E., Moharrami, M., Lakestani, M.Fractional order Alpert ...
  • Hashemi, M.S., Baleanu, D.Lie symmetry analysis of fractional differential equations, ...
  • He, S., Sun, K., Wang, H.Dynamics of the fractional-order Lorenz ...
  • Heris, J.M.Solving the integro-differential equations using the modified Laplace Adomian ...
  • Hesameddini, E., Rahimi, A., Asadollahifard, E.On the convergence of a ...
  • Hesameddini, E., Riahi, M., Latifizadeh, H.A coupling method of homotopy ...
  • Hesameddini, E., Shahbazi, M.Hybrid Bernstein block-pulse functions for solving system ...
  • Liu, Z., Cheng, A., Li, X.A second-order finite difference scheme ...
  • Mahdy, A.M., Mohamed, E.M.Numerical studies for solving system of linear ...
  • Miller, K.S., Ross, B.An introduction to the fractional calculus and ...
  • Modanli, M., Akgül, A.On solutions of fractional order telegraph partial ...
  • Mohyud-Din, S.T., Khan, H., Arif, M., Rafiq, M.Chebyshev wavelet method ...
  • Nazari S.D., Jahanshahi, M.Numerical solution of nonlinear fractional Volterra-Fredholm integro-differential ...
  • Nazari, D., Shahmorad, S.Application of the fractional differential transform method ...
  • Oldham, K., Spanier, J.The fractional calculus theory and applications of ...
  • Ordokhani, Y., Rahimi, N.Numerical solution of fractional Volterra integro-differential equations ...
  • Pashayi, S., Hashemi, M.S., Shahmorad, S.Analytical Lie group approach for ...
  • Pirim, N.A., Ayaz, F.A new technique for solving fractional order ...
  • Podlubny, I.Fractional differential equations: an introduction to fractional derivatives, fractional ...
  • Sahu, P., Ray, S.S.A novel Legendre wavelet Petrov-Galerkin method for ...
  • Samko, S.G., Kilbas, A.A., Marichev, O.I. Fractional integrals and derivatives, ...
  • Shah, K., Khan, Z.A., Ali, A., Amin, R., Khan, H., ...
  • Singh, B.K.Homotopy perturbation new integral transform method for numeric study ...
  • Sweilam, N., Nagy, A., Youssef, I.K., Mokhtar, M.M.New spectral second ...
  • Wang, Y., Zhu, L.Solving nonlinear Volterra integro-differential equations of fractional ...
  • Yin, X.B., Kumar, S., Kumar, D.A modified homotopy analysis method ...
  • Zhu, L., Fan, Q. Solving fractional nonlinear Fredholm integro-differential equations ...