Haar Wavelets Approach For Solving Multidimensional Stochastic Itô-Volterra Integral Equations∗ (original) (raw)

Numerical Solution of Stochastic Volterra-Fredholm Integral Equations Using Haar Wavelets

2016

In this paper, we present a computational method for solving stochastic VolteraFredholm integral equations which is based on the Haar wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are worked out. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and reliability of the proposed method.

A Efficient Computational Method for Solving Stochastic Itô-Volterra Integral Equations

2015

In this paper, a new stochastic operational matrix for the Legendre wavelets is presented and a general procedure for forming this matrix is given. A computational method based on this stochastic operational matrix is proposed for solving stochastic Itô-Voltera integral equations. Convergence and error analysis of the Legendre wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.

A computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations

2016

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method was demonstrated by some non-trivial examples and comparison with the block pulse functions method.

Wavelets and Linear Algebra 4(2) (2017) 33-48 Wilson wavelets for solving nonlinear stochastic integral equations

2000

MSC: 60H20, 65T60. Abstract A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic Itô-Volterra integral equations. To do this a new stochastic operational matrix of Itô integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration , the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the efficiency and accuracy of the proposed method. c ⃝ (2017) Wavelets and Linear Algebra

Numerical approach for solving stochastic Volterra–Fredholm integral equations by stochastic operational matrix

2012

In this paper, we obtain stochastic operational matrix of block pulse functions on interval [0, 1) to solve stochastic Volterra-Fredholm integral equations. By using block pulse functions and their stochastic operational matrix of integration, the stochastic Volterra-Fredholm integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is O(h). Furthermore, the results show that the approximate solutions have a good degree of accuracy.

A novel efficient technique for solving nonlinear stochastic Itô–Volterra integral equations

Expert Systems with Applications, 2024

There is a growing need of stochastic integral equations (SIEs) to investigate the behavior of complex dynamical systems. Since real-world phenomena frequently dependent on noise sources, modeling them naturally necessitates the use of SIEs. As most SIEs cannot be solved explicitly, thus the behaviors of the studied systems are investigated using approximate solutions of their SIEs. Despite the fact that this problem has been soundly investigated and numerous methods have been presented, the practice demonstrated that obtaining satisfied approximations is not always guaranteed, necessitating the development of new effective techniques. This paper gives a new technique for solving nonlinear Itô-Volterra SIEs by reducing them to linear or nonlinear algebraic systems via the power of a combination of generalized Lagrange functions and Jacobi-Gauss collocation points. The accuracy and reliability of the new technique are evaluated and compared with the existing techniques. Moreover, sufficient conditions to make the estimate error tends to zero are given. The new technique shows surprisingly high efficiency over the existing techniques in terms of computational efficiency and approximation capability. The accuracy of the solution based on the new technique is much higher than that via the existing techniques. The required time of the new technique is much less than that of the existing techniques, where, in some circumstances, the existing techniques take more than 20 times as long as the new technique.

Numerical Approximation of Stochastic Volterra-Fredholm Integral Equation using Walsh Function

arXiv (Cornell University), 2023

In this paper, a computational method is developed to find an approximate solution of the stochastic Volterra-Fredholm integral equation using the Walsh function approximation and its operational matrix. Moreover, convergence and error analysis of the method is carried out to strengthen the validity of the method. Furthermore, the method is numerically compared to the block pulse function method and the Haar wavelet method for some non-trivial examples.