Date of Award
Bachelor of Science (B.S.) in Mathematics and University Honors
Mathematics and Statistics
Diffusion, Convection, Variable Separation, Python Code, PDE
A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic equation to determine all the eigenvalues. Thirdly, we use Python to construct and illustrate the solutions for all the cases based on the newly developed solution formulas. Finally, we share all the associated Python code for public access.
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Glinowiecka-Cox, Małgorzata B., "Analytic Solution of 1D Diffusion-Convection Equation with Varying Boundary Conditions" (2022). University Honors Theses. Paper 1182.