The present paper proposes a fast numerical method for the linear Volterra integral equations with regular and weakly singular kernels having smooth solutions. This method is based on the approximation of the kernel, to simplify the integral operator and then discretization of the simplified operator using a forward difference formula. To analyze and verify the accuracy of the method, we examine sample and benchmark problems with known exact solutions.
Jalalvand,M , Jazbi,B and Mokhtarzadeh,M R . (2013). A finite difference method for the smooth solution of linear Volterra integral equations. International Journal of Nonlinear Analysis and Applications, 4(2), 1-10. doi: 10.22075/ijnaa.2013.19
MLA
Jalalvand,M , , Jazbi,B , and Mokhtarzadeh,M R . "A finite difference method for the smooth solution of linear Volterra integral equations", International Journal of Nonlinear Analysis and Applications, 4, 2, 2013, 1-10. doi: 10.22075/ijnaa.2013.19
HARVARD
Jalalvand M, Jazbi B, Mokhtarzadeh M R. (2013). 'A finite difference method for the smooth solution of linear Volterra integral equations', International Journal of Nonlinear Analysis and Applications, 4(2), pp. 1-10. doi: 10.22075/ijnaa.2013.19
CHICAGO
M Jalalvand, B Jazbi and M R Mokhtarzadeh, "A finite difference method for the smooth solution of linear Volterra integral equations," International Journal of Nonlinear Analysis and Applications, 4 2 (2013): 1-10, doi: 10.22075/ijnaa.2013.19
VANCOUVER
Jalalvand M, Jazbi B, Mokhtarzadeh M R. A finite difference method for the smooth solution of linear Volterra integral equations. IJNAA. 2013;4(2):1-10. doi: 10.22075/ijnaa.2013.19
International Journal of Nonlinear Analysis and Applications