supplement high-order elements of A matrix

Author: WenyinWei

include/integrators/ode/dop853.hpp

@@ -175,7 +175,36 @@ class DOP853Integrator : public AdaptiveIntegrator<S, T> {
         A_[7][4] = static_cast<time_type>(1.07262030446373284651809199168e-1); // a85
         A_[7][5] = static_cast<time_type>(-1.53194377486244017527936158236e-2); // a86
         A_[7][6] = static_cast<time_type>(8.27378916381402288758473766002e-3); // a87
-        // ... (fill in all A_[8][*], A_[9][*], A_[10][*], A_[11][*] as needed)
+        
+        A_[8][0] = 3.70920001185047927108779319836e-2;
+        A_[8][3] = 1.70383925712239993810214054705e-1;
+        A_[8][4] = 1.07262030446373284651809199168e-1;
+        A_[8][5] = -1.53194377486244017527936158236e-2;
+        A_[8][6] = 8.27378916381402288758473766002e-3;
+
+        A_[9][0] = 6.24110958716075717114429577812e-1;
+        A_[9][3] = -3.36089262944694129406857109825;
+        A_[9][4] = -8.68219346841726006818189891453e-1;
+        A_[9][5] = 2.75920996994467083049415600797e1;
+        A_[9][6] = 2.01540675504778934086186788979e1;
+        A_[9][7] = -4.34898841810699588477366255144e1;
+
+        A_[10][0] = 4.77662536438264365890433908527e-1;
+        A_[10][3] = -2.48811461997166764192642586468;
+        A_[10][4] = -5.90290826836842996371446475743e-1;
+        A_[10][5] = 2.12300514481811942347288949897e1;
+        A_[10][6] = 1.52792336328824235832596922938e1;
+        A_[10][7] = -3.32882109689848629194453265587e1;
+        A_[10][8] = -2.03312017085086261358222928593e-2;
+
+        A_[11][0] = -9.3714243008598732571704021658e-1;
+        A_[11][3] = 5.18637242884406370830023853209;
+        A_[11][4] = 1.09143734899672957818500254654;
+        A_[11][5] = -8.14978701074692612513997267357;
+        A_[11][6] = -1.85200656599969598641566180701e1;
+        A_[11][7] = 2.27394870993505042818970056734e1;
+        A_[11][8] = 2.49360555267965238987089396762;
+        A_[11][9] = -3.0467644718982195003823669022;
 
         // B coefficients for final solution (Fortran b1, b6, b7, ...)
         B_[0] = static_cast<time_type>(5.42937341165687622380535766363e-2); // b1