Adding a New Equation
Phaser provides an Equation Editor with a graphical interface for adding new equations; it can be accessed by choosing Add Custom Equation item from the Equation menu of the Main Application window. Once entered successfully, a new equation is deposited into Custom Equation Library of Phaser and is indistinguishable, as far as the user is concerned, from the permanent library equations. Previously added user-defined Custom Equations can also easily be modified or deleted.
Full details of the Equation Editor is available in PhaserHelp. As a quick reference, here is a list of tips:
- Equation Name: Pick a name for your equation.
- Equation Type: PHASER is designed for ODEs or MAPs. Make sure you pick the correct type appropriate for your equation. For MAPs the only Algorithm is Iteration. For ODEs there are many Algorithms to choose from as default; you can change your default Algorithm later from the Numerics Editor.
- Parameters:Any lower case letter, except t and x, which are reserved for time and space, and any upper case letter, except E, which is reserved for the famous constant, can be used as a parameter. Click on the text field and type. Enter a default value for your parameter and click Add Parameter. Now the Parameter List field should show the parameter and its default value. To remove a parameter from the Parameter List, highlight the desired parameter by clicking on it and then push the Remove Parameter button. You can add upto several dozen parameters, if you need them.
- Equation Expressions: To enter the first equation x1' = for ODE and x1 -> for MAP, click on the text field and type. To enter an additional equation, first activate the second equation x2' = by pressing the small button to the left of it, then click on its text field and type. The maximum number of equations in a set is 24.
Variables: x1, x2, ..., x24 are used for variables.
Operators: + for addition, - for subtraction or unary minus, * for multiplication, / for division, ^ for power, % for remainder.
Many standard mathematical functions, such as abs(), exp(), log(), sin(), are provided.
- Initial Conditions: Each equation is provided with a set of default initial conditions. The right-most short text field next to x1 = is for the default initial condition of the first variable x1; click on it and type. Initial conditions for other variables are entered in a similar manner.
- Apply: Remember Apply. At this point, Phaser tries to parse your Equation Expressions. Any errors are reported in the Status field. If all goes well, your equation is added to Custom Equation Library.