[PDF] MATLAB Ordinary Differential Equation (ODE) solver for a simple





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MATLAB Ordinary Differential Equation (ODE) solver for a simple

equation) can be troublesome especially when one deals with coupled (multiple) differential equations which have to be solved simultaneously.



MATLAB Ordinary Differential Equation (ODE) solver for a simple

equation) can be troublesome especially when one deals with coupled (multiple) differential equations which have to be solved simultaneously.



On MATLAB command: dsolve

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MATLAB Ordinary Differential Equation (ODE) solver for a simple example

1. Introduction

Differential equations are a convenient way to express mathematically a change of a dependent variable

(e.g. concentration of species A) with respect to an independent variable (e.g. time). When writing a

differential equation, one operate on the rates of change of quantities rather than the quantities

themselves. This simplifies greatly the derivation of important relationships used by engineers around the

world. However, switching from the rates of change to the values themselves (i.e. solving a differential

equation) can be troublesome, especially when one deals with coupled (multiple) differential equations

which have to be solved simultaneously. In many cases, an analytical solution does not exist and engineers

have to rely on numerical (approximate) solutions.

A special and very abundant group of differential equations is called ordinary differential equations

(ODEs). In these equations, dependent variables are functions of one independent variable only, for example: where the rate of change of the concentration of species A over time is directly proportional to the concentration of species A. One may also think of a system of ODEs, where two or more dependent variables exist, each of them expressed as a separate ODE, for example:

F@?஺

F@?஻

Systems of equations similar to these shown above are very common in CRE problems, therefore it is

advisable to learn how to solve them in order to predict the evolution of variables in time or space (e.g.

length of the reactor). In this tutorial we will solve a simple ODE and compare the result with analytical

solution. In another tutorial (see Ordinary Differential Equation (ODE) solver for Example 12-1 in MATLAB tutorials on the CRE website) we tackle a system of ODEs where more than one dependent variable changes with time.

2. Developing a simple model with ODE to solve

We will now develop a simple model of an isothermal CSTR (see Figure to the right) operated at non-steady state where a second-order, irreversible elementary reaction takes place:

The rate constant is ݇Lrquotesdbs_dbs21.pdfusesText_27

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