{"id":18,"date":"2025-03-13T15:09:20","date_gmt":"2025-03-13T15:09:20","guid":{"rendered":"https:\/\/people.mtsu.edu\/akhaliq\/?page_id=18"},"modified":"2026-04-30T19:43:43","modified_gmt":"2026-05-01T00:43:43","slug":"research-interest","status":"publish","type":"page","link":"https:\/\/people.mtsu.edu\/akhaliq\/research-interest\/","title":{"rendered":"Research Interest"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Numerical Partial Differential Equations<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Data driven models<\/li>\n\n\n\n<li>Solving PDEs with deep learning<\/li>\n\n\n\n<li>Time-Space Fractional Partial Differential Systems<\/li>\n\n\n\n<li>Discontinuous Galerkin Methods<\/li>\n\n\n\n<li>Efficient Implicit-Explicit Time Stepping Methods<\/li>\n\n\n\n<li>Adaptive methods<\/li>\n\n\n\n<li>Mesh free approximation using Radial Bases Functions<\/li>\n\n\n\n<li>Numerical methods for Stochastic Partial Differential Equations<\/li>\n\n\n\n<li>Numerical methods for Stiff Stochastic Differential Equations<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Current Application Areas of Research<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Scientific Machine Learning\n<ul class=\"wp-block-list\">\n<li>Solving PDEs with deep learning<\/li>\n\n\n\n<li>Data driven models with Noisy data<\/li>\n\n\n\n<li>Parameter estimation and inverse problems<\/li>\n\n\n\n<li>Mathematical and scinetific machine learning<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Computational Finance\n<ul class=\"wp-block-list\">\n<li>Pricing complex financial derivatives in high dimensions<\/li>\n\n\n\n<li>Models with Stochastic Volatility and Transaction Cost<\/li>\n\n\n\n<li>Regime Switching with Jumps<\/li>\n\n\n\n<li>High Performance Computing is Finance<\/li>\n\n\n\n<li>Numerical Methods for Estimating Risk Measures<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Computational Bio Chemical Systems\n<ul class=\"wp-block-list\">\n<li>Large scale Reaction Diffusion systems, Complex Pattern Formation<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Computational Stochastic Analysis\n<ul class=\"wp-block-list\">\n<li>Numerical analysis of Stochastic Ordinary and Partial Differential Equations.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Computational Modeling in Optics\n<ul class=\"wp-block-list\">\n<li>System of Non-linear Schrodinger Equations<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Numerical Partial Differential Equations Current Application Areas of Research<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-18","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/pages\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/comments?post=18"}],"version-history":[{"count":1,"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/pages\/18\/revisions"}],"predecessor-version":[{"id":180,"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/pages\/18\/revisions\/180"}],"wp:attachment":[{"href":"https:\/\/people.mtsu.edu\/akhaliq\/wp-json\/wp\/v2\/media?parent=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}