Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions

2021 ◽  
Author(s):  
Leijie Qiao ◽  
Da Xu ◽  
Bo Tang ◽  
Jun Zhou
Keyword(s):  
Evolution Equation ◽  
Difference Schemes ◽  
Three Dimensions ◽  
Weakly Singular Kernels ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Weakly Singular ◽  
Nonlocal Evolution Equation ◽  
Singular Kernels

Simulating waves in flows by Runge-Kutta and compact difference schemes

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 421-429 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Kwang-Chung Hsieh ◽  
Y.-L. Peter Tsai
Keyword(s):  
Difference Schemes ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Runge Kutta

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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