Treffer: Leveraging the power of Java and Matlab to solve ODEs.

Ordinary Differential Equations (ODE) are used to model a wide range of physical processes. An ODE is an equation containing a function of one independent variable and its ordinary derivatives. This paper presents the development and application of a practical teaching module introducing java programming techniques to electronics, computer, and bioengineering students before they encounter digital signal processing and its applications in junior and senior level courses. This paper will focus primarily on how to solve ODEs using Java and Matlab programming tools. There are two basic types of boundary condition categories for ODEs -- initial value problems and two-point boundary value problems. Initial value problems are simpler to solve because you only have to integrate the ODE one time. The solution of a two- point boundary value problem usually involves iterating between the values at the beginning and end of the range of integration. Runge-Kutta schemes are among the most commonly used techniques to solve initial-value problem ODEs. Matlab also presents several tools for modeling linear systems. These tools can be used to solve differential equations arising in such models, and to visualize the input-output relations. This paper attempts to describe how to use Java programming tool to solve initial value problems of ordinary differential equations (ODEs) using the Runge-Kutta scheme. It will also discuss how to represent initial value problems and demonstrate how to apply Matlab's ODE solvers to such problems. It will also explain how to select a solver and how to specify solver options for efficient, customized execution. This paper provides an introduction to the Ordinary Differential Equations(ODEs). After a quick overview of selected numerical methods for solving differential equations using Matlab, we will briefly give an account of Euler and modified Euler methods for solving first order differential equations. This will be followed by numerical method for systems specially Runge- Kutta schemes and applications of second order differential equations in mechanical vibrations and electric circuits by leveraging the power of Java and Matlab. This paper will explain how this learning and teaching module is instrumental for progressive learning of students; the paper will also demonstrate how the numerical and integral algorithms are derived and computed through leverage of the java data structures. As a result, there will be a discussion concerning the comparison of Java and Matlab programming as well as students' feedback. The result of this new approach is expected to strengthen the capacity and quality of our undergraduate degree programs and enhance overall student learning and satisfaction. [ABSTRACT FROM AUTHOR]

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