Input Syntax

  To use taylor, the first order of business is to prepare an input ASCII file with the system of ODEs. Input to taylor consists of statements of the form

      id = expr;
      diff(var, tvar) = expr;

where tvar is the time variable and expr is a valid mathematical expression made from numbers, the time variable, the state variables, elementary functions , , , , , , , , and , using the four arithmetic operators and function composition. For example

     a = sin(1) + log(1 + exp(-0.5));
     b = a + cos(0.1);
     c = a+b;
     ff = sin(x+t) * exp(-x*x);
     diff(x,t) = c * ff - tan(t);

are all valid statements.

Taylor also understands if-else expressions and non-nested sums. For example, taylor accepts the following statements:

      ss = sum( i*sin(i * x)+ i *cos(i*t), i=1,10);
      diff(x,t) = ss;
      diff(y,t) = if(y>t) {  if(y>0.0) { y } else { 1-y }  }
                  else    { y+t};

The detailed input syntax is given in Appendix A.