By Bruce A. Finlayson
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Extra resources for Nonlinear Analysis in Chemical Engineering
3-4811). 1. (3-651, from the interpolation formulas. Eqs. 0-48b) and 0-54 ). 3-6 Solve the following problem from 1 = O to r = I as a test of your computer programming. Use II l o e d �� with a lix�>d step size. I'll N El: RIN(; ISSlS IN l'lll' M LCA I. 1 -1 �an� n;;l ;::�� : �� ��'. ;:;�:::�:�::·:::;::�;; : � ·'"' St>h'C . h1s. '. 'l 5 ) usmJ_l the •11me three inLcgrntio ns11u1ts 1c1i•·c11 in fa1s. O . 5( T, - T, J + fiR , , �c.!. 0 P = O. pi = l . 73 ;· = 30 Lc = O. 9 Develop the cquanons � �� - �- - R (c) = O Pcdx 2 :� Jx (l) = 0 c ( I ) _.
1 111 Ordinary Differemiol Equorio11s. 1971. 4. J005'J, R1•1. I Comp1llt•r /J11crmr1:m111i111r, 1975 L: 22, II . Ii. o 1 4, pp. 63 11. J'J74 594··597, 1976. :tcn1cd b) o t dinar) difTcrential equations. usually ol second order. :ondition-;.
1 r" . d" r·· .. Jr. +h (3·53) (3-54) y'(oi:)dct The integration schemes are generated by inserting various interpolation ronnulas ror dy/d1('X)=r'(:x). Subs1itution of Eq. into Eq. +li ;�o a,V;y� (3-54) ii o:(oi:+l) ... (IX+i-1) Ill J Jo i! +11)'�+ i)+.. � )'�+.. +/tf(\'nJ+Q(/12) The formula is more revealing in the form Yn+_�1-Yn,,,, /(y J+O(li) . 1he slope . vel and extend that slope to the next time level to obtain J�+ J'n· � 26 NONLINEAR ANALYSIS IN CHEMICAL ENGINEERING Yn•L )'. / ;,. rallon methods.
Nonlinear Analysis in Chemical Engineering by Bruce A. Finlayson