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International Journal of Computer Mathematics Volume 93, 2016 - Issue 9
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Original Articles

Wavelets Galerkin method for solving stochastic heat equation

M.H. HeydariFaculty of Mathematics, Yazd University, Yazd, Iran;The Laboratory of Quantum Information Processing, Yazd University, Yazd, IranCorrespondence[email protected]
,
M.R. HooshmandaslFaculty of Mathematics, Yazd University, Yazd, Iran;The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran
,
Gh. Barid LoghmaniFaculty of Mathematics, Yazd University, Yazd, Iran
&
C. CattaniDepartment of Mathematics, University of Salerno, Fisciano, Italy
Pages 1579-1596 | Received 01 Dec 2014, Accepted 15 Jun 2015, Published online: 04 Aug 2015

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F. Soltani Sarvestani, M. H. Heydari, A. Niknam & Z. Avazzadeh. (2019) A wavelet approach for the multi-term time fractional diffusion-wave equation. International Journal of Computer Mathematics 96:3, pages 640-661.
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Articles from other publishers (35)

M. H. Heydari, Sh. Zhagharian & C. Cattani. (2024) A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations. Mathematical Methods in the Applied Sciences 47:6, pages 4530-4549.
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Parisa Rahimkhani. (2024) Deep Neural Network for Solving Stochastic Biological Systems. Iranian Journal of Science.
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M.H. Heydari, Sh. Zhagharian & M. Razzaghi. (2024) Discrete Chebyshev polynomials for the numerical solution of stochastic fractional two-dimensional Sobolev equation. Communications in Nonlinear Science and Numerical Simulation 130, pages 107742.
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Xueli Zhang, Jin Huang & Xiaoxia Wen. (2024) A new numerical algorithm based on least squares method for solving stochastic Itô-Volterra integral equations. Numerical Algorithms.
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Jizeng Wang, Xiaojing Liu & Youhe Zhou. (2024) Application of Wavelet Methods in Computational Physics. Annalen der Physik.
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M.H. Heydari, Sh. Zhagharian & M. Razzaghi. (2023) Jacobi polynomials for the numerical solution of multi-dimensional stochastic multi-order time fractional diffusion-wave equations. Computers & Mathematics with Applications 152, pages 91-101.
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Yadollah Ordokhani & Nasrin Samadyar. (2023) Approximating a New Class of Stochastic Differential Equations via Operational Matrices of Bernoulli Polynomials. Iranian Journal of Science 47:5-6, pages 1633-1647.
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Santanu Saha Ray & Reema Gupta. (2023) A novel numerical approach based on shifted second‐kind Chebyshev polynomials for solving stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel. Mathematical Methods in the Applied Sciences 46:13, pages 14026-14044.
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Tahereh Eftekhari & Jalil Rashidinia. (2023) A new hybrid approach for nonlinear stochastic differential equations driven by multifractional Gaussian noise. Mathematical Methods in the Applied Sciences 46:12, pages 13469-13484.
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S. Raja Balachandar, D. Uma, H. Jafari & S.G. Venkatesh. (2023) Numerical solution for stochastic heat equation with Neumann boundary conditions. Thermal Science 27:Spec. issue 1, pages 57-66.
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D. Uma, H. Jafari, S Raja Balachandar & S. G. Venkatesh. (2022) An Approximation Method for Stochastic Heat Equation Driven by White Noise. International Journal of Applied and Computational Mathematics 8:6.
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M. H. Heydari & O. Bavi. (2021) An efficient wavelet method for nonlinear problems arising in heat transfer. Engineering with Computers 38:S4, pages 2867-2878.
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Farshid Mirzaee, Shadi Rezaei & Nasrin Samadyar. (2021) Solution of time‐fractional stochastic nonlinear sine‐Gordon equation via finite difference and meshfree techniques. Mathematical Methods in the Applied Sciences 45:7, pages 3426-3438.
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Seddigheh Banihashemi, Hossein Jafaria & Afshin Babaei. (2022) A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay. Discrete & Continuous Dynamical Systems - S 15:2, pages 339.
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Mohamed A. Abdelkawy, Hijaz Ahmad, Mdi Begum Jeelani & Abeer S. Alnahdi. (2021) Fully Legendre spectral collocation technique for stochastic heat equations. Open Physics 19:1, pages 921-931.
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Farshid Mirzaee, Erfan Solhi & Shiva Naserifar. (2021) Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method. Applied Mathematics and Computation 410, pages 126447.
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Lingyun He, Seddigheh Banihashemi, Hossein Jafari & Afshin Babaei. (2021) Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme. Chaos, Solitons & Fractals 149, pages 111018.
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Farshid Mirzaee, Shadi Rezaei & Nasrin Samadyar. (2020) Solving one‐dimensional nonlinear stochastic Sine‐Gordon equation with a new meshfree technique . International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 34:4.
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Farshid Mirzaee & Sahar Alipour. (2021) Bicubic B-Spline Functions to Solve Linear Two-Dimensional Weakly Singular Stochastic Integral Equation. Iranian Journal of Science and Technology, Transactions A: Science 45:3, pages 965-972.
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Farshid Mirzaee, Khosro Sayevand, Shadi Rezaei & Nasrin Samadyar. (2020) Finite Difference and Spline Approximation for Solving Fractional Stochastic Advection-Diffusion Equation. Iranian Journal of Science and Technology, Transactions A: Science 45:2, pages 607-617.
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Farshid Mirzaee & Nasrin Samadyar. (2020) Implicit meshless method to solve 2D fractional stochastic Tricomi‐type equation defined on irregular domain occurring in fractal transonic flow . Numerical Methods for Partial Differential Equations 37:2, pages 1781-1799.
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Igor E. Poloskov. Transitional processes in linear stochastic parabolic and hyperbolic systems with constant delays. Transitional processes in linear stochastic parabolic and hyperbolic systems with constant delays.
R. Roohi, M. H. Heydari, O. Bavi & H. Emdad. (2019) Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects. Engineering with Computers 37:1, pages 579-595.
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Nasrin Samadyar, Yadollah Ordokhani & Farshid Mirzaee. (2020) Hybrid Taylor and block-pulse functions operational matrix algorithm and its application to obtain the approximate solution of stochastic evolution equation driven by fractional Brownian motion. Communications in Nonlinear Science and Numerical Simulation 90, pages 105346.
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Afshin Babaei, Hossein Jafari & S. Banihashemi. (2020) A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. Symmetry 12:6, pages 904.
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J. Calatayud, J.-C. Cortés, J.A. Díaz & M. Jornet. (2020) Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme. Applied Numerical Mathematics 151, pages 413-424.
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Aydin Secer & Neslihan Ozdemir. (2019) An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation. Advances in Difference Equations 2019:1.
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Farshid Mirzaee & Nasrin Samadyar. (2019) Numerical Solution of Time Fractional Stochastic Korteweg–de Vries Equation via Implicit Meshless Approach. Iranian Journal of Science and Technology, Transactions A: Science 43:6, pages 2905-2912.
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Neslihan Ozdemir, Aydin Secer & Mustafa Bayram. (2019) The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative. Mathematics 7:6, pages 486.
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Faruk Dusunceli. (2019) New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model. Advances in Mathematical Physics 2019, pages 1-9.
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M H Heydari, M R Hooshmandasl & C Cattani. (2018) A new operational matrix of fractional order integration for the Chebyshev wavelets and its application for nonlinear fractional Van der Pol oscillator equation. Proceedings - Mathematical Sciences 128:2.
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Fakhrodin Mohammadi. (2017) Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets. Boletim da Sociedade Paranaense de Matemática 35:1, pages 195.
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Z. Taheri, S. Javadi & E. Babolian. (2017) Numerical solution of stochastic fractional integro-differential equation by the spectral collocation method. Journal of Computational and Applied Mathematics 321, pages 336-347.
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Fuqiang Zhao, Jiaquan Xie & Qingxue Huang. (2017) Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet. Discrete Dynamics in Nature and Society 2017, pages 1-10.
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M. H. Heydari, M. R. Hooshmandasl, A. Shakiba & C. Cattani. (2016) Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations. Nonlinear Dynamics 85:2, pages 1185-1202.
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