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International Journal of Computer Mathematics Volume 89, 2012 - Issue 18: RECENT ADVANCES ON THE NUMERICAL SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
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Section B

Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains

Petru A. Cioica FB Mathematik und Informatik, Philipps-Universität Marburg, D-35032, Marburg, GermanyCorrespondence[email protected]
&
Stephan Dahlke FB Mathematik und Informatik, Philipps-Universität Marburg, D-35032, Marburg, Germany
Pages 2443-2459 | Received 11 Jul 2011, Accepted 20 Sep 2011, Published online: 25 Nov 2011

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Farshid Mirzaee, Nasrin Samadyar & Seyede Fatemeh Hoseini. (2017) A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation. Applicable Analysis 96:13, pages 2163-2179.
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Peter Kloeden & Klaus Ritter. (2012) Preface: ‘Recent advances in the numerical approximation of stochastic partial differential equations’. International Journal of Computer Mathematics 89:18, pages 2441-2442.
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Hanan A. Alkhidhr. (2023) Characteristics of stochastic solutions for the chiral NLSE through Brownian motion process. AIP Advances 13:11.
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R.A. Alomair, S.Z. Hassan, Mahmoud A.E. Abdelrahman, Ali H. Amin & E.K. El-Shewy. (2022) New solitary optical solutions for the NLSE with -potential through Brownian process . Results in Physics 40, pages 105814.
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Somayeh Abdi-Mazraeh, Hossein Kheiri & Safar Irandoust-Pakchin. (2021) Construction of operational matrices based on linear cardinal B-spline functions for solving fractional stochastic integro-differential equation. Journal of Applied Mathematics and Computing 68:1, pages 151-175.
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Nasrin Samadyar, Yadollah Ordokhani & Farshid Mirzaee. (2020) The couple of Hermite-based approach and Crank-Nicolson scheme to approximate the solution of two dimensional stochastic diffusion-wave equation of fractional order. Engineering Analysis with Boundary Elements 118, pages 285-294.
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M. Ahmadinia, H. Afshari A.M. Heydari. (2019) Numerical solution of Itô-Volterra integral equation by least squares method. Numerical Algorithms 84:2, pages 591-602.
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Farshid Mirzaee & Sahar Alipour. (2020) Cubic B-spline approximation for linear stochastic integro-differential equation of fractional order. Journal of Computational and Applied Mathematics 366, pages 112440.
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Farshid Mirzaee & Sahar Alipour. (2019) An efficient cubic B‐spline and bicubic B‐spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations. Mathematical Methods in the Applied Sciences 43:1, pages 384-397.
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Shayan Aziznejad & Julien Fageot. (2020) Wavelet analysis of the Besov regularity of Lévy white noise. Electronic Journal of Probability 25:none.
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Sami Ullah Khan, Mushtaq Ali & Ishtiaq Ali. (2019) A spectral collocation method for stochastic Volterra integro-differential equations and its error analysis. Advances in Difference Equations 2019:1.
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Farshid Mirzaee & Nasrin Samadyar. (2018) Using radial basis functions to solve two dimensional linear stochastic integral equations on non-rectangular domains. Engineering Analysis with Boundary Elements 92, pages 180-195.
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Farshid Mirzaee & Sahar Alipour. (2018) Approximate solution of nonlinear quadratic integral equations of fractional order via piecewise linear functions. Journal of Computational and Applied Mathematics 331, pages 217-227.
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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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M.H. Heydari, M.R. Hooshmandasl, C. Cattani & F.M. Maalek Ghaini. (2015) An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics. Journal of Computational Physics 283, pages 148-168.
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M.H. Heydari, M.R. Hooshmandasl, F.M. Maalek Ghaini & C. Cattani. (2014) A computational method for solving stochastic It??Volterra integral equations based on stochastic operational matrix for generalized hat basis functions. Journal of Computational Physics 270, pages 402-415.
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Petru A. Cioica, Stephan Dahlke, Nicolas Döhring, Stefan Kinzel, Felix Lindner, Thorsten Raasch, Klaus Ritter & René L. Schilling. 2014. Extraction of Quantifiable Information from Complex Systems. Extraction of Quantifiable Information from Complex Systems 83 107 .
Petru Cioica, Kyeong-Hun Kim, Kijung Lee & Felix Lindner. (2013) On the $L_q(L_p)$-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains. Electronic Journal of Probability 18:none.
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