While the well-researched Finite Difference Method (FDM) discretizes every independent variable into algebraic equations, Method of Lines discretizes all but one dimension, leaving an Ordinary Differential Equation (ODE) in the remaining dimension. That way, ODE's numerical methods can be applied to solve Partial Differential Equations (PDEs). In this project, Linear Multistep Methods and Method of Lines are used to numerically solve the heat equation. Specifically, the explicit Adams-Bashforth method and the implicit Backward Differentiation Formulas are implemented as Alternative Finite Difference Schemes. We also examine the consistency of these schemes.
"On the Consistency of Alternative Finite Difference Schemes for the Heat Equation,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 23:
1, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss1/2