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Numerical Analysis and Computation Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Numerical Analysis and Computation
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Numerical Analysis Of A Model For The Growth Of Microorganisms, Alexander Craig Montgomery, Braden J. Carlson
Rose-Hulman Undergraduate Mathematics Journal
A system of first-order differential equations that arises in a model for the growth of microorganisms in a chemostat with Monod kinetics is studied. A new, semi-implicit numerical scheme is proposed to approximate solutions to the system. It is shown that the scheme is uniquely solvable and unconditionally stable, and further properties of the scheme are analyzed. The convergence rate of the numerical solution to the true solution of the system is given, and it is shown convergence of the numerical solutions to the true solutions is uniform over any interval [0, T ] for T > 0.
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
Rose-Hulman Undergraduate Mathematics Journal
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.
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Rose-Hulman Undergraduate Mathematics Journal
We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.