Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
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S. Saha Ray
and
S. Singh
Abstract
In this article, the numerical solutions of stochastic Volterra–Fredholm integral equations have been obtained by hybrid Legendre block-pulse functions (BPFs) and stochastic operational matrix. The hybrid Legendre BPFs are orthonormal and have compact support on
References
[1] K. Maleknejad, B. Basirat and E. Hashemizadeh, Hybrid Legendre polynomials and Block-Pulse functions approach for nonlinear Volterra–Fredholm integro-differential equations, Comput. Math. Appl. 61 (2011), 2821–2828.10.1016/j.camwa.2011.03.055Search in Google Scholar
[2] A.-M. Wazwaz, A first course in integral equations, World Scientific Publishing, London, 2015.10.1142/9570Search in Google Scholar
[3] C.P. Tsokos and W.J. Padgett, Random Integral Equations with Applications to Life Sciences and Engineering, Academic Press, New York, 1974.Search in Google Scholar
[4] G.J. Lord, C.E. Powell and T. Shardlow, An Introduction to Computational Stochastic PDEs, Cambridge University Press, New York, USA, 2014.10.1017/CBO9781139017329Search in Google Scholar
[5] B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 5th ed, Springer-Verlag, New York, 1998.10.1007/978-3-662-03620-4Search in Google Scholar
[6] J.C. Cortés, L. Jordan and L. Villafuerte, Numerical solution of random differential equations: A mean square approach, Math. Comput. Model. 45 (2007), 757–765.10.1016/j.mcm.2006.07.017Search in Google Scholar
[7] D.J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev. 43(3) (2001), 525–546.10.1137/S0036144500378302Search in Google Scholar
[8] P.E. Kloeden and E. Platen, Numerical solution of stochastic differential equations, Springer-Verlag, New York, 1992.10.1007/978-3-662-12616-5Search in Google Scholar
[9] K. Maleknejad, M. Khodabin and M. Rostami, Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions, Math. Comput. Model. 55 (2012), 791–800.10.1016/j.mcm.2011.08.053Search in Google Scholar
[10] M. Khodabin, K. Maleknejad, M. Rostami and M. Nouri, Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix, Comput. Math. Appl. 64 (2012), 1903–1913.10.1016/j.camwa.2012.03.042Search in Google Scholar
[11] K. Maleknejad, E. Hashemizadeh and B. Basirat, Numerical solvability of Hammerstein integral equations based on hybrid Legendre and Block-Pulse functions, Int. Conf. Parallel Distrib. Process. Tech. Appl. 2010 (2010), 172–175.Search in Google Scholar
[12] K. Maleknejad and M.T. Kajani, Solving second kind integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions, Appl. Math. Comput. 145 (2003), 623–629.10.1016/S0096-3003(03)00139-5Search in Google Scholar
[13] S. Saha Ray and A.K. Gupta, Numerical solution of fractional partial differential equation of parabolic type with Dirichlet boundary conditions using two-dimensional Legendre wavelets method, J. Comput. Nonlinear Dynam. 11 (1) (2016), 9.10.1115/1.4028984Search in Google Scholar
[14] F. Mohammadi and P. Adhami, Numerical study of stochastic Volterra-Fredholm integral equations by using second kind Chebyshev wavelets, Random Operators Stochastic Equ. 24(2) (2016), 129–141.10.1515/rose-2016-0009Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay
- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
- Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy
- Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach
- A Novel Macromodel based on Krylov Subspace Projection Method for Micromixers with Serpentine Channels
- Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities
- Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
- Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems
- Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms
- Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses
- Analysis of a Delayed Predator–Prey System with Harvesting
- Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
- Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline
- Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well
- Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller
- A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation
- RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil
- Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
- Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation
Articles in the same Issue
- Frontmatter
- A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay
- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
- Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy
- Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach
- A Novel Macromodel based on Krylov Subspace Projection Method for Micromixers with Serpentine Channels
- Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities
- Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
- Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems
- Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms
- Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses
- Analysis of a Delayed Predator–Prey System with Harvesting
- Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
- Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline
- Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well
- Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller
- A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation
- RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil
- Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
- Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation
