University of TabrizComputational Methods for Differential Equations2345-39827320190701Unknown functions estimation in a parabolic equation arises from Diffusion Tensor Magnetic Resonance Imaging3833959010ENFahimehSoltanianDepartment of Mathematics, Payame Noor University,
P. O. Box 19395-3697, Tehran, Iran0000-0003-3068-3378MortezaGarshasbiDepartment of Mathematics, Iran University of Science
and Technology, P. O. Box 16846-13114, Tehran, IrannullJournal Article20180710In this work, a general mathematical model of Diffusion Tensor Magnetic Resonance Imaging is formulated as an inverse problem. An effective numerical approach based on space marching method and mollifcation scheme is established to solve this problem. Convergence and stability of proposed approach are established. Using two test problems, the robustness and ability of the numerical approach is investigated.https://cmde.tabrizu.ac.ir/article_9010_b8fa1ddb8daa253fb30ef6300dcfaf9e.pdf