Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

2001 ◽  
Vol 39 (3) ◽  
pp. 957-982 ◽  
Author(s):  
Hermann Brunner ◽  
Arvet Pedas ◽  
Gennadi Vainikko
Keyword(s):  
Differential Equations ◽  
Collocation Methods ◽  
Piecewise Polynomial ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Polynomial Collocation

Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels

2008 ◽  
Vol 8 (3) ◽  
pp. 207-222 ◽  
Author(s):  
H. BRUNNER
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Optimal Order ◽  
Piecewise Polynomial ◽  
Fully Discrete ◽  
Proportional Delays ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Discrete Galerkin Method ◽  
Polynomial Collocation

AbstractWe analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays. It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.

scholarly journals Solving a System of Fractional-Order Volterra-Fredholm Integro-Differential Equations with Weakly Singular Kernels via the Second Chebyshev Wavelets Method

2021 ◽  
Vol 5 (3) ◽  
pp. 70
Author(s):  
Esmail Bargamadi ◽  
Leila Torkzadeh ◽  
Kazem Nouri ◽  
Amin Jajarmi
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Algebraic System ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Chebyshev Wavelets ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Chebyshev Wavelet

In this paper, by means of the second Chebyshev wavelet and its operational matrix, we solve a system of fractional-order Volterra–Fredholm integro-differential equations with weakly singular kernels. We estimate the functions by using the wavelet basis and then obtain the approximate solutions from the algebraic system corresponding to the main system. Moreover, the implementation of our scheme is presented, and the error bounds of approximations are analyzed. Finally, we evaluate the efficiency of the method through a numerical example.

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