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Overfull \hbox (1.70041pt too wide) in paragraph at lines 410--416 \OT1/cmr/m/n/12 plane cir-cu-lar re-stricted three-body prob-lem, to com-pare v ar-i-ous fourth- [] Overfull \hbox (3.40231pt too wide) in paragraph at lines 410--416 \OT1/cmr/m/n/12 order Runge-Kutta for-mu-las with each other and with \OT1/cmr/ m/sc/12 Mat-lab\OT1/cmr/m/n/12 's \OT1/cmtt/m/n/12 ode45\OT1/cmr/m/n/12 . [] Overfull \hbox (9.73688pt too wide) detected at line 429 [] [] [8] Overfull \hbox (118.99597pt too wide) detected at line 492 [] [] [9] Underfull \vbox (badness 10000) has occurred while \output is active [] [10] File: trunc_trees.eps Graphic file (type eps) Overfull \hbox (37.48499pt too wide) in paragraph at lines 514--515 [] [] File: ErrvsEff.eps Graphic file (type eps) Overfull \hbox (37.48499pt too wide) in paragraph at lines 521--522 [] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [11] Underfull \hbox (badness 10000) in paragraph at lines 523--524 [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 %*********************************************************** **************[] [] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 % dfun String that names a function M-file for derivatives[] [] [12] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 % c [optional] Two-component vector: c(1) is "c2" and c (2) is "c3"[] [] Overfull \hbox (23.24666pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 % This will become a more natural indexing : c1,c2,c3,c4[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 % y Solution of DE (4th-order approximation) on the mesh x[] [] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 % xspan = [0, 6.19216933]; y0 = [1.2; 0; 0; -1.04935750983 031990726];[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 %*********************************************************** **************[] [] Overfull \hbox (17.9967pt too wide) in paragraph at lines 747--747 []\OT1/cmtt/m/n/10 if nargin < 6 % Provide default values for optiona l parameters[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [13] Overfull \hbox (17.9967pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 b1 = 1/12*(1+6*c2*c3-2*c2-2*c3) / (c2*c3); % Formulas for b's and a's[] [] Overfull \hbox (2.24684pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 b2 = -1/12*(-1+2*c3) / (c2*(c2-1)*(c3-c2)); % determined b y reduced[] [] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 b3 = 1/12*(2*c2-1) / (c3*(c3-1)*(c3-c2)); % Groebner bas is elements[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 b4 = 1/12*(6*c2*c3-4*c2+3-4*c3) / ((c2-1)*(c3-1)); % calcu lated by Maple[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [14] Overfull \hbox (23.24666pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 h = min([h abs(xf-x0)/8]); % h is at most 1/8 of integra tion interval[] [] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 k24 = h*feval(dfun,x(n)+(1+c4)*h,ynp1 +(a41*k21+a42*k22 +a43*k23));[] [] Overfull \hbox (12.74675pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 kd4 = 2*h*feval(dfun,x(n)+2*c4*h,y(n,:)'+(a41*kd1+a42*kd2 +a43*kd3));[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [15] Overfull \hbox (2.24684pt too wide) in paragraph at lines 747--747 [] \OT1/cmtt/m/n/10 if mod(n,32)==0 % Allocate more space for solution[] [] Underfull \vbox (badness 10000) has occurred while \output is active [] [16] Overfull \hbox (28.49661pt too wide) in paragraph at lines 797--797 []\OT1/cmtt/m/n/10 %*********************************************************** **************[] [] Overfull \hbox (17.9967pt too wide) in paragraph at lines 797--797 []\OT1/cmtt/m/n/10 % column vectors evaluated at the x components (so y(:,i) = y(x_i)), and[] [] Overfull \hbox (17.9967pt too wide) in paragraph at lines 797--797 []\OT1/cmtt/m/n/10 % dy is a matrix of n column vectors of first derivative val ues computed[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 797--797 []\OT1/cmtt/m/n/10 % *(x-x(2) + ... + f(2*n)(x-x(1))^2*...*(x-x(n-2)) ^2*(x-x(n-1)),[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 797--797 []\OT1/cmtt/m/n/10 %*********************************************************** **************[] [] Overfull \hbox (28.49661pt too wide) in paragraph at lines 797--797 [] \OT1/cmtt/m/n/10 f = NaN; 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