Setting

Setting

• Solver : Selection and detailed settings of numerical integration.

• Solver : selection of ODE solver built in MATLAB is possible.

 ode45 This is based on an explicit Runge-Kutta formula, the Dormand-Prince pair. It is a one-step solver; that is, in computing y(tn), it needs only the solution at the immediately preceding time point, y(tn-1). In general, ode45 is the best solver to apply as a "first try" for most problems. ode23 This is also based on an explicit Runge-Kutta proposed by Bogacki and Shampine. It may be more efficient than ode45 at crude tolerances and in the presence of mild stiffness. ode23 is a one-step solver. ode113 This is a variable order Adams-Bashforth-Moulton PECE solver. It may be more efficient than ode45 at stringent tolerances. ode113 is a multi-step solver; that is, it normally needs the solutions at several preceding time points to compute the current solution. ode23s}; This is based on a modified Rosenbrock formula of order 2. Because it is a one-step solver, it may be more efficient than ode15s at crude tolerances. It can solve some kinds of stiff problems for which ode15s is not effective. ode15s This is a variable order solver based on the numerical differentiation formulas (NDFs). These are related to but are more efficient than the backward differentiation formulas, BDFs (also known as Gear's method). Like ode113, ode15s is a multi-step method solver. If you suspect that a problem is stiff or if ode45 failed or was very inefficient, try ode15s. myself This is a standard fixed step 4th order Runge Kutta method．It is not recommended unless under particular circumstances.

• Relative tolerance : measures the error relative to the size of each state. The relative tolerance represents a percentage of the state's value.
• Absolute tolerance : s a threshold error value. This tolerance represents the acceptable error as the value of the measured state approaches zero*1.
• Step type : selection of the step size method used by the Solver
• Variable : use a variable step size (Default)
• Invariable : use a fixed step size
• Initial step : By default, the solvers select an initial step size by examining the derivatives of the states at the start time. If the first step size is too large, the solver may step over important behavior. The initial step size parameter is a suggested first step size. The solver tries this step size but reduces it if error criteria are not satisfied.
• Solver frequency : Time for the solver to complete one calculation(Not available).
• Time direction： The time direction to run the numerical integration. + is the positive direction of the time, while - is the negative drection of one.

• Parameter : associate a key to a particular parameter adjustment.

• You can assign keys to parameters in the alphabetic order．You can also select a key for each parameter in the associated pull tab.
• a parameter increase is associated to an upper case letter，a decrease to a lower case letter.
• the default value for both increase or decrease granularity is set to 0.1. In case of modification, please enter the desired value.

• Window : drawing window's setting options

• Add New Window : in case you want to create an extra drawing window, clicking this button will create a new one.

• X-axis : you can select as the x-axis either time t or any of the state variables, x[1], x[2], ... , x[n].
• Y-axis : you can select as the y-axis any of the state variables, x[1], x[2], ... , x[n].
• range : the default setting Auto-scale of the drawing range adjusts this setting automatically. However, if you want to visualize the system response in a fixed range, this option makes it possible.

• Line : Adjustment of the drawing line width and color.
• line color : selection of the line color． It can be set through the RGB value．It is also possible to press the line color button to display a color palette．You can then select any color from this palette.
• width : setting of the line width. The unit is pt.
• Point : adjustment of the size and color of the points representing potential fixed points or periodic points.
• point color : selection of the point color. It can be set through the RGB value．It is also possible to press the point color button to display a color palette．You can then select any color from this palette.
• size : setting of the point size. The unit is pt.

• Poincare : detailed settings of the Poincare section.

• sub map： This option is used to control the display of the point of the Poincare map. The first point is displayed as a red point. In the case that the osillatory solution has multi-period, other sampling points than the first one are represented as green points in the default setting. The sub map switch decides whether or not represents the green point(Default setting is On.).

• color : selection of the point color of the other point than the first crossing point. It can be set through the RGB value．It is also possible to press the point color button to display a color palette．You can then select any color from this palette.

• Equation : this option is used to verify the equations of the analyzed nonautonomous system.

*1 for detail see odeset

Last-modified: 2009-07-23 (Thu) 20:13:30 (3650d)