In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the...In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.展开更多
The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By a...The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.展开更多
We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the assoc...We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.展开更多
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approxima...While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.展开更多
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of ...The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.展开更多
文摘In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.
文摘The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.
文摘We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.
文摘While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.
文摘The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
