Solving Volterra Integral Equations of the Second Kind with Convolution Kernel
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (2005)] to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad et al. [K. Maleknejad and T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, Indian J. Pure Appl. Math. (2014)] to gain the approximate solutions of systems of second kind Volterra integral equations with the help of Taylor expansion method. The Taylor expansion method transforms the integral equation into a linear ordinary differential equation (ODE) which, in this case, requires specified boundary conditions. Boundary conditions can be determined using the integration technique instead of differentiation technique. This method is more stable than derivative method and can be implemented to obtain an approximate solution of the Volterra integral equation with smooth and weakly singular kernels. An error analysis for the method is provided. A comparison between our obtained results and the previous results is made which shows that the suggested method is accurate enough and more stable.
The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space
In this paper, to solve a linear one-dimensional Volterra integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of integral equation in terms of the basis functions. The examples presented in this ...متن کامل
Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems
The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp). The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system. In this article, the obtained nonlinear system has been solved as a dynamical system. The solution of the obtained nonlinear system by the dynamical system throug...متن کامل
This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...متن کامل
Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis of such equations is estimating the eff...متن کامل
We consider a piecewise constant nite element approximation to the convolution Volterra equation problem of the second kind: nd u such that u = f + u in a time interval 0; T ]. An a posteriori estimate of the error measured in the W ?1 p (0; T) norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples are given for problems in w...متن کامل
دوره 13 شماره 1
صفحات 63- 69
تاریخ انتشار 2021-09-01
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