* System of nonlinear equations * Equilibrium combustion (Meintjes and Morgan, 1990) * 1 known solution * Sets SET i /1*5/; * Parameters SCALAR p / 40 /; SCALAR R / 10 /; SCALAR R5 ; SCALAR R6 ; SCALAR R7 ; SCALAR R8 ; SCALAR R9 ; SCALAR R10 ; SCALAR k5 / 0.193 /; SCALAR k6 / 0.002597 /; SCALAR k7 / 0.003448 /; SCALAR k8 / 1.799e-05 /; SCALAR k9 / 0.0002155 /; SCALAR k10 / 3.846e-05 /; R5 = k5; R6 = k6*p**(-0.5); R7 = k7*p**(-0.5); R8 = k8 / p; R9 = k9*p**(-0.5); R10 = k10 / p; VARIABLES y(i) s objval objective function variable; FREE VARIABLES objval; EQUATIONS f Objective function h1 h2p h2m h3p h3m h4p h4m h5p h5m; f .. objval =e=s; h1 .. y('1') - 3*y('5') + y('1')*y('2') =e= 0; h2p .. y('1') + R8*y('2') - R*y('5') - s + 3*R10*POWER(y('2'),2) + 2*y('1')*y('2') + R7*y('2')*y('3') + R9*y('2')*y('4') + y('2')*POWER(y('3'),2) =l= 0; h2m .. -y('1') - R8*y('2') + R*y('5') - s -3*R10*POWER(y('2'),2) -2*y('1')*y('2') - R7*y('2')*y('3') - R9*y('2')*y('4') -y('2')*POWER(y('3'),2) =l= 0; h3p .. R6*y('3') - 8*y('5') - s + 2*R5*POWER(y('3'),2) + R7*y('2')*y('3') + 2*y('2')*POWER(y('3'),2) =l= 0; h3m .. -R6*y('3') + 8*y('5') - s -2*R5*POWER(y('3'),2) -R7*y('2')*y('3') -2*y('2')*POWER(y('3'),2) =l= 0; h4p .. -4*R*y('5') - s + 2*POWER(y('4'),2) + R9*y('2')*y('4') =l= 0; h4m .. 4*R*y('5') - s -2*POWER(y('4'),2) -R9*y('2')*y('4') =l= 0; h5p .. y('1') + R8*y('2') + R6*y('3') - s + R10*POWER(y('2'),2) + R5*POWER(y('3'),2) + POWER(y('4'),2) + y('1')*y('2') + R7*y('2')*y('3') + R9*y('2')*y('4') + y('2')*POWER(y('3'),2) =l= 1; h5m .. -y('1') - R8*y('2') - R6*y('3') - s -R10*POWER(y('2'),2) -R5*POWER(y('3'),2) -POWER(y('4'),2) -y('1')*y('2') - R7*y('2')*y('3') - R9*y('2')*y('4') -y('2')*POWER(y('3'),2) =l= -1; * Bounds y.LO(i) = 0.0001; y.UP(i) = 100; MODEL test /ALL/; SOLVE test USING NLP MINIMIZING objval;