Problem description

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We see that the mathematical input data are:

• the provenience of the problem - it is a test problem or a model for a real phenomena, i.e. it has been mentioned somewhere;
• the number of ODEs, in our case, n;
• the independent variable name, t for example;
• the dependent variable name, y for example. If we have more that one equations, this variable is a n-dimensional vector. Usually, if each component represents a physical measure, different names are taken (I for intensity, C for capacity and so on). Also, if the system is large, simple letters are not enough to describe the equations, and indexed variables are used (for example, y₁ , ... , y_n). In both cases, a finite set of dependent variables can be enumerated;
• the system function f, is a vector of n mathematical expressions. Each expression can include only the dependent variables, mathematical functions, and arithmetic operators;
• the integration interval, defined by two values, the minimum and the maximum value for the independent variable, t₀ and t₀+T;
• the initial values (y₀) - n real values must enumerated, each corresponding to a dependent variable.