Positivity-Preserving Non-Standard Schemes For Nonlinear Partial Differential Equations
Keywords:
nonlinear Partial Differential Equation, Non-standardAbstract
This study investigates the development and application of non-standard finite difference schemes designed to preserve positivity when solving nonlinear partial differential equations (PDEs). The proposed methodologies address challenges related to the stability, boundedness, and physical relevance of numerical solutions for nonlinear PDEs frequently arising in engineering and scientific modeling. Emphasis is placed on constructing discretization techniques that ensure the solutions remain positive and bounded, maintaining key qualitative properties of the underlying continuous models. Numerical experiments are conducted to verify the effectiveness and accuracy of the presented schemes, demonstrating improvements over traditional finite difference approaches
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