A numerical solution for a quasi solution of the time-fractional stochastic backward parabolic equation

DOI10.1016/j.cam.2023.115441zbMath1527.65088OpenAlexW4384208032MaRDI QIDQ6049261

Azim Aminataei, Tayebeh Nasiri, Ali Zakeri

Publication date: 17 October 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2023.115441

zbMATH Keywords

existence and uniquenessCaputo fractional derivativeLevenberg-Marquardt regularizationquasi solution2D Chebyshev waveletstime-fractional stochastic backward parabolic equation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10) Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) Inverse problems for PDEs (35R30) Best approximation, Chebyshev systems (41A50) Numerical methods for wavelets (65T60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
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• Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems
• Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients
• Inverse source problem for time-fractional diffusion with discrete random noise
• Space-time fractional stochastic partial differential equations
• Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems
• The regularizing Levenberg-Marquardt scheme is of optimal order
• Solution of stochastic nonlinear time fractional PDEs using polynomial chaos expansion combined with an exponential integrator
• Moment theory and some inverse problems in potential theory and heat conduction
• An inverse coefficient problem for a nonlinear parabolic variational inequality
• A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
• An Arzela-Ascoli type theorem for random functions
• Uniqueness for an inverse source problem of determining a space dependent source in a time-fractional diffusion equation
• On a backward problem for nonlinear fractional diffusion equations
• Existence of solutions for nonlinear fractional stochastic differential equations
• Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
• On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis
• A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms
• An efficient numerical method based on Euler wavelets for solving fractional order pantograph Volterra delay-integro-differential equations
• Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions
• A Sobolev space theory for stochastic partial differential equations with time-fractional derivatives
• An inverse time-dependent source problem for a time-space fractional diffusion equation
• A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms
• An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
• Application of wavelet collocation method for hyperbolic partial differential equations via matrices
• Fracture mechanics. Inverse problems and solutions.
• A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary-value problems
• Finite element method for space-time fractional diffusion equation
• Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers
• A finite element method for time fractional partial differential equations
• Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems
• HIGHER-ORDER PARAMETER UNIFORM CONVERGENT SCHEMES FOR ROBIN TYPE REACTION-DIFFUSION PROBLEMS USING ADAPTIVELY GENERATED GRID
• The Fractional Calculus for Some Stochastic Processes
• Fractional Partial Differential Equations and Their Numerical Solutions
• Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data
• FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
• The nonlinear Rayleigh‐Stokes problem with Riemann‐Liouville fractional derivative
• Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis
• A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis
• On a backward problem for nonlinear time fractional wave equations
• A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems
• Existence and regularity results of a backward problem for fractional diffusion equations
• A higher order difference method for singularly perturbed parabolic partial differential equations
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Variational formulation for the stationary fractional advection dispersion equation
• A numerical method for backward parabolic problems with non-selfadjoint elliptic operators

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