Discipline: Mathematics & Statistics
Subcategory: STEM Research
Abhinandan Chowdhury - Savannah State University
Co-Author(s): Leo Degon, Savannah State University
In this work, we seek the numerical solution of the Gardner equation (combined KdV–mKdV equation) which studies various areas of physics including plasma physics, fluid dynamics, quantum field theory, solid state physics and others. We aim to solve some initial boundary value problems constructed for the Gardner equation by the modified exponential time differencing method proposed by kassam and Trefethen. The test problems are derived from some analytical studies to validate the efficiency and accuracy of the suggested method. Accuracy of the employed numerical scheme for this class of equations is assessed in terms of global relative error and L_∞ error norms. Numerical experiments demonstrate the accuracy and robustness of the method which can be further used for solving other nonlinear problems.
Funder Acknowledgement(s): NSF-HBCU-UP: Catalyst Project 1-800798
Faculty Advisor: None Listed,