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Full-Text Articles in Physical Sciences and Mathematics
Stability And Convergence For Nonlinear Partial Differential Equations, Oday Mohammed Waheeb
Stability And Convergence For Nonlinear Partial Differential Equations, Oday Mohammed Waheeb
Boise State University Theses and Dissertations
If used cautiously, numerical methods can be powerful tools to produce solutions to partial differential equations with or without known analytic solutions. The resulting numerical solutions may, with luck, produce stable and accurate solutions to the problem in question, or may produce solutions with no resemblance to the problem in question at all. More such numerical computations give no hope of solving this troublesome feature and one needs to resort to investing time in a theoretical approach. This thesis is devoted not solely to computations, but also to a theoretical analysis of the numerical methods used to generate computationally the …
Perfect Stripes From A General Turing Model In Different Geometries, Jean Tyson Schneider
Perfect Stripes From A General Turing Model In Different Geometries, Jean Tyson Schneider
Boise State University Theses and Dissertations
We explore a striped pattern generated by a general Turing model in three different geometries. We look at the square, disk, and hemisphere and make connections between the stripes in each spatial direction. In particular, we gain a greater understanding of when perfect stripes can be generated and what causes defects in their patterns. In this investigation, we look at the difference between the solutions due to the different domain shapes. In the end, we propose a reason why stripes from a reaction-diffusion system with zero-flux boundary conditions can be perfect on a square or hemisphere, but not on a …