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Numerical Solutions of Direct and Inverse Problems for a Time Fractional Viscoelastoplastic Equation

Tatar, Salih / Tnaztepe, Ramazan / Zeki, Mustafa

This paper is devoted to numerical solutions of direct and inverse problems for the nonlinear nonlocal time fractional equation $\partial^{β} / \partial t^{β} u (x, y, t) - \nabla \cdot [f (T^{2}) \nabla u] = 2 t$ , where $T^{2} = | \nabla u |^{2}$ . After solving the direct problem by the method of lines, a numerical method based on discretization of the minimization problem, steepest descent method, and least-squares approach is proposed for the solution of the inverse problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent.

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Numerical Solutions of Direct and Inverse Problems for a Time Fractional Viscoelastoplastic Equation

Tatar, Salih / Tnaztepe, Ramazan / Zeki, Mustafa

This paper is devoted to numerical solutions of direct and inverse problems for the nonlinear nonlocal time fractional equation $\partial^{β} / \partial t^{β} u (x, y, t) - \nabla \cdot [f (T^{2}) \nabla u] = 2 t$ , where $T^{2} = | \nabla u |^{2}$ . After solving the direct problem by the method of lines, a numerical method based on discretization of the minimization problem, steepest descent method, and least-squares approach is proposed for the solution of the inverse problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent.

Numerical Solutions of Direct and Inverse Problems for a Time Fractional Viscoelastoplastic Equation

Tatar, Salih / Tnaztepe, Ramazan / Zeki, Mustafa

This paper is devoted to numerical solutions of direct and inverse problems for the nonlinear nonlocal time fractional equation $\partial^{β} / \partial t^{β} u (x, y, t) - \nabla \cdot [f (T^{2}) \nabla u] = 2 t$ , where $T^{2} = | \nabla u |^{2}$ . After solving the direct problem by the method of lines, a numerical method based on discretization of the minimization problem, steepest descent method, and least-squares approach is proposed for the solution of the inverse problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent.

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Title:

Numerical Solutions of Direct and Inverse Problems for a Time Fractional Viscoelastoplastic Equation

Contributors:

Tatar, Salih (author) / Tnaztepe, Ramazan (author) / Zeki, Mustafa (author)

Published in:

Journal of Engineering Mechanics ; 143

Publication date:

2017-02-23

ISSN:

0733-9399 , 1943-7889

DOI:

https://doi.org/10.1061/(ASCE)EM.1943-7889.0001239

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

Unknown

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