First Advisor

Bin Jiang

Date of Award

Spring 6-16-2022

Document Type


Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors


Mathematics and Statistics




Differential equations, Partial -- Numerical solutions, Separation of variables




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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This work benefitted from the Research Training Group (RTG) activities under NSF grant DMS-2136228.

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