Method of Lines
Posted on March 17, 2022 Mathematical Modeling
Many of the systems and processes we work with for our clients can be modeled with mathematical models.
By applying reasonable approximations, we can arrive at a simpler system of equations. These “simpler systems of equations” are, nonetheless, still complex enough to require numerical solutions. The reduced systems are typically a system of partial differential and algebraic equations.
One method for solving these is the method of lines. This involves the discretization of either the spatial or time variable to reduce the partial different equations to a system of ordinary differential equations. The advantage is that once an appropriate method of lines formulation is worked out, we can then leverage the vast selection of existing and optimized numerical integration schemes and software packages for solving systems of ordinary differential equations to solve our reformulated system.
When applicable, we employ the methods of lines with the mathematical models that we develop for our clients. This allows us to employ sophisticated algorithms, while also saving time to go from model formulation to obtaining model results.