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Meade, Andrew J., Jr. Dick, Andrew J. Nagarajaiah, Satish Mokhtarzadeh, Arya 2014-09-22T20:35:56Z 2014-09-22T20:35:56Z 2014-05 2014-02-20 May 2014 2014-09-22T20:35:56Z Mokhtarzadeh, Arya. "Solution of the Fokker-Planck Equation by Sequentially Optimized Meshfree Approximation." (2014) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77226">https://hdl.handle.net/1911/77226</a>. https://hdl.handle.net/1911/77226 This thesis presents a technique to solve the Fokker-Planck equation by applica- tion of the Sequentially Optimized Meshfree Approximation (SOMA) method. It is well known that numerical solution of the Fokker-Planck equation is made di cult by the challenges of positivity enforcement, in nite domain, and high dimensionality. Through the use of optimization, radial basis functions, and its mesh-free architecture, respectively, the SOMA method attempts to address these challenges and sidestep the exponential growth of dimensionality, which hinders traditional numerical methods. Results are presented for one, two, and four-dimensional Fokker-Planck equations. This work will show that SOMA allows for enforcement of a positivity condition that removes the need for log-transforms, produces a solution domain that does not re- quire arti cial boundary condition enforcement, and provides the capability of solving higher dimensional forms of the Fokker-Planck equation. application/pdf eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. Fokker-Planck equation FPE Sequentially optimized meshfree approximation SOMA Oscillator Curse of dimensionality Positivity Radial basis functions Series expansion Optimization Solution of the Fokker-Planck Equation by Sequentially Optimized Meshfree Approximation Thesis Text Mechanical Engineering and Materials Science Engineering Rice University Masters Master of Science open.access