Landweber Iterative Method for an Inverse Source Problem of Time-Space Fractional Diffusion-Wave Equation
Fan Yang, Yan Zhang, Xiaoxiao Li
Abstract
Abstract In this paper, we apply a Landweber iterative regularization method to determine a space-dependent source for a time-space fractional diffusion-wave equation from the final measurement. In general, this problem is ill-posed, and a Landweber iterative regularization method is used to obtain the regularization solution. Under the a priori parameter choice rule and the a posteriori parameter choice rule, we give the error estimates between the regularization solution and the exact solution, respectively. Some numerical results in the one-dimensional and two-dimensional cases show the utility of the used regularization method.
Topics & Concepts
Regularization (linguistics)A priori and a posterioriMathematicsInverse problemIterative methodApplied mathematicsWell-posed problemMathematical analysisMathematical optimizationComputer sciencePhilosophyEpistemologyArtificial intelligenceFractional Differential Equations SolutionsNumerical methods in engineeringNumerical methods in inverse problems