Regularization of a terminal value problem for time fractional diffusion equation
Nguyen Anh Triet, Vo Van Au, Le Dinh Long, Dumitru Bǎleanu, Nguyen Huy Tuan
Abstract
In this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill‐posed in the sense of Hadamard, so the quasi‐boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one‐dimensional and two‐dimensional case show the evidence of the used regularization method.
Topics & Concepts
MathematicsRegularization (linguistics)Hadamard transformA priori and a posterioriInverse problemWell-posed problemBoundary value problemApplied mathematicsDiffusion equationMathematical analysisMathematical optimizationComputer scienceArtificial intelligenceService (business)PhilosophyEconomyEconomicsEpistemologyFractional Differential Equations SolutionsNumerical methods in engineeringIterative Methods for Nonlinear Equations