Application Guide

euler ()
Catalog >
euler(Expr, Var, depVar, {Var0, VarMax},
depVar0, VarStep [, eulerStep]) ⇒ matrix
euler(SystemOfExpr, Var, ListOfDepVars,
{Var0, VarMax}, ListOfDepVars0,
VarStep [, eulerStep]) ⇒ matrix
euler(ListOfExpr, Var, ListOfDepVars,
{Var0, VarMax},ListOfDepVars0,
VarStep [, eulerStep]) ⇒ matrix
Uses the Euler method to solve the system
with depVar(Var0)=depVar0 on the
interval [Var0,VarMax]. Returns a matrix
whose first row defines the Var output
values and whose second row defines the
value of the first solution component at the
corresponding Var values, and so on.
Expr is the right-hand side that defines the
ordinary differential equation (ODE).
SystemOfExpr is the system of right-hand
sides that define the system of ODEs
(corresponds to order of dependent
variables in ListOfDepVars).
ListOfExpr is a list of right-hand sides that
define the system of ODEs (corresponds to
the order of dependent variables in
ListOfDepVars).
Var is the independent variable.
ListOfDepVars is a list of dependent
variables.
{Var0, VarMax} is a two-element list that
tells the function to integrate from Var0 to
VarMax.
ListOfDepVars0 is a list of initial values
for dependent variables.
Differential equation:
y'=0.001*y*(100-y) and y(0)=10
To see the entire result, press £ and then
use ¡and¢ to move the cursor.
Compare above resultwith CAS exact
solution obtained using deSolve() and
seqGen():
System of equations:
with y1(0)=2 andy2(0)=5
Alphabetical Listing 61