## File: dblint.dem

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maxima 5.6-17
 `12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455` ``````/* Example of use of double integrator (DBLINT) */ /* F must be a function of two variables, R and S must be functions of one variable, and A and B must be floating point numbers (all of the functions must be translated or compiled prior to using DBLINT) */ /* Get the fasl file containing DBLINT(F,R,S,A,B) */ batchload("dblint"); /* To get the double integral of exp(x-y^2) over the region bounded by y=1 and y=2+x and x=0 to x=1 */ /* Define the integrand as a function of two variables */ F(X,Y):=(MODE_DECLARE([X,Y],FLOAT),EXP(X-Y^2)); /* Define the lower and upper limits on the inner (y in this case) integral as a function of the outer variable (x in this case) */ R(X):=(MODE_DECLARE(X,FLOAT),1.0); S(X):=(MODE_DECLARE(X,FLOAT),2.0+X); /* Now translate these functions for the sake of efficiency */ TRANSLATE(F,R,S); /* Call the DBLINT function with quoted arguments for function names, and floating point values for the endpoints of the outer (x) integration */ DBLINT_ANS:DBLINT('F,'R,'S,0.0,1.0); /* Compare with the exact answer */ INTY:RISCH(EXP(X-Y^2),Y); XINT:EV(INTY,Y:2+X)-EV(INTY,Y:1); DINT:RISCH(XINT,X); ANS:EV(DINT,X:1.0)-EV(DINT,X:0.0),NUMER; /* Relative error check here */ (ANS-DBLINT_ANS)/ANS; /* Quite reasonable */ /* Of course, the DBLINT routine will still work even when we choose an area over which the closed-form integral fails to be expressible in terms of standard transcendental functions */ S1(X):=(MODE_DECLARE(X,FLOAT),2.0+X^(3/2)); TRANSLATE(S1); DBLINT('F,'R,'S1,0.0,1.0); /* To see what happens when this integral is attempted in closed-form, you may BATCH(DBLINT,DEMO1,DSK,SHARE1), and that will also show sample use of FLOATDEFUNK and QUANC8 */ "end of dblint.dem"\$ ``````