At this Mathematics and Applications Seminar, hear from Professor Kuppalapalle Vajravelu in the Department of Mathematics as he explains a semi-analytical method and its application to systems of nonlinear ODEs and PDEs arising in science and engineering models.

This discussion is intended for graduate students in science and engineering. 

Abstract:
A semi-analytical method, that is, the optimal homotopy analysis method (OHAM) for the solutions of nonlinear differential equations arising in science and engineering models will be presented. To obtain accurate analytical solutions, multiple auxiliary linear operators will be considered which permit accuracy with relatively a few terms. The convergence control parameters will be selected through the construction of an optimal control problem for the minimization of the accumulated residual errors. Also, open questions related to OHAM will be discussed.

Furthermore, a Directly Defining the Inverse Mapping Method (MDDiM) to obtain solutions to nonlinear systems arising in combined free and forced convection flows will be presented. Errors ranging from five decimal accuracy to ten decimal accuracy will be obtained with relatively a few terms. The idea is novel and is not limited to solving ordinary differential equations: The method can be applied to solve systems of partial differential equations. Recently published papers on this topic will be discussed. 

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The UCF Mathematics and Applications Seminar, which takes place every Friday from 11 a.m. to 12 p.m. in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.