Master’s Thesis at the University of Basrah Explores Two-Stage Hybrid Methods for Nonlinear Stochastic Differential Equations
A master’s thesis at the College of Science, University of Basrah, entitled “Two-Stage Hybrid Methods for Nonlinear Stochastic Differential Equations”, investigated advanced numerical approaches for solving nonlinear stochastic differential equations (SDEs).
The thesis, presented by Mohammed Imad Abdulkarim, aimed to develop two novel hybrid numerical methods to solve nonlinear SDEs with greater efficiency and improved accuracy.
The study proposed two innovative methods. The first is the fourth-order Chebyshev–Runge–Kutta method, which approximates local Brownian increments using Chebyshev polynomials, followed by the application of the classical fourth-order Runge–Kutta method.
The second method is the Ito-corrected fourth-order Chebyshev–Runge–Kutta method, which applies the Ito correction formula to the drift term, followed by a numerical hybridization to incorporate higher-order stochastic effects.
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