# Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems
## Appendix A
### Coefficients of AP40434 ig  
\[\mathbf{c^{T}}=\left(\frac{139}{1159},\frac{11}{19},\frac{1375}{2014}\right)\]  
\[A_{0}=\begin{pmatrix}-482.1874750642102&4.750000000000000&-5.916666666666667&-6.5 000000000000000\\ 5295.612100386801&78.73229010791468&60.16394904407432&7.2222222222222\\ 893.8003010294580&-4.061724320422766&9.736228361340601&19.67879886925837\\ -5707.694317901957&-68.66254446706468&-58.05689396607474&-35.61626763467349 \end{pmatrix}\]  
\[K_{0}=\begin{pmatrix}-49.91295086094522&0.5250000000000000&-3.439024390243902&2. 894736842105263\\ 405.5730073881453&49.31516975831240&8.193548387096774&-3.428571428571429\\ 53.62032171809015&12.67084977396168&-1.304859285573478&4.013292871986014\\ -414.6382351541371&-49.0887063383948&-1.334271117642095&-15.23643896150272 \end{pmatrix}\]  
\[A=\begin{pmatrix}-2.604429828805958\\ 6.603320924494022&11.44234275562775\\ 0.5317173544040980&-2.710438820206414&3.55000000000000\\ -5.0000000000000000&2.026117385005894&2.376616772673509&-15.21524654319290 \end{pmatrix}\]  
\[K=\text{diag}(-0.8973222553064913,3.337407156628221,1.164566261468968,-2.604651162790 698)\]\[A_{N}=\begin{pmatrix}-3.754385964912281&0.01222493887530562&1.014925373134328&-0.1403 508771929825\\ 11.35280296428295e&45.64990373363066&-15.17493010383148&-20.79910559459065\\ 0.03205698176794144&2.937595714981687&-3.756123160591242&2.666624105937791\\ -7.630473981138614&-48.59972438748765&18.91612789128839&18.27283236584584\\ \end{pmatrix}\]  
\[K_{N}=\begin{pmatrix}-0.9578456075353955&-0.3387096774193548&0.119402985074626 9&0.8045112781954887\\ 11.57142857142857&-96.60667975350700&-20.1250000000000&102.4846028390543\\ 3.761888534906390&-33.44512959236514&-5.865106921633463&34.94704625261853\\ -15.32045224098695&134.2026156894527&26.37615509001594&-141.3196101415549\\ \end{pmatrix}\]  
_Appendix A.4. Coefficients of AP4043 die_  
\[A_{0}=\begin{pmatrix}\dfrac{1573}{27}\\ -\dfrac{29140496694667}{1728480384000}&\dfrac{37071572404007}{69715375488000}& \dfrac{37246788257}{8450348544}\\ -\dfrac{98934973036237}{2160600480000}&-\dfrac{59311823623513}{87144219360000}& \dfrac{51770824817}{13203669600}\\ \dfrac{7653678714559}{1387052160000}&-\dfrac{787257354487}{38730764160000}&- \dfrac{32557703329}{23473190400}&\dfrac{18014543}{144484600}\\ \end{pmatrix}\]  
\[K_{0}=\begin{pmatrix}\dfrac{110}{9}\\ \dfrac{4}{5}&\dfrac{168095353644187}{920242956441600}&-\dfrac{136571614975979} {36809718257664}\\ -\dfrac{9857504559041}{1080300240000}&\dfrac{398472962076949}{1150303695520000}& -\dfrac{18235836500357}{18404859128832}\\ -\dfrac{1423069729157}{1440400320000}&\dfrac{398472962076949}{766869130368000}& \dfrac{136571614975979}{61349530429440}&\dfrac{2}{61}\\ \end{pmatrix}\]  
\[A=\begin{pmatrix}\dfrac{45808744223}{19505421000}\\ -\dfrac{279428522}{187552125}&\dfrac{3}{4}\\ \dfrac{285647}{15004170}&\dfrac{22704013}{125034750}&-\dfrac{11}{10}\\ \dfrac{1}{4}&-\dfrac{11824391}{41678250}&\dfrac{832579}{4167825}&\dfrac{18014543 }{144484600}\\ \end{pmatrix}\]  
\[K=\text{diag}\Big{(}\dfrac{35085281}{25006950^{\prime}}\dfrac{2300653}{335650^{ \prime}}-\dfrac{1780019}{2500695^{\prime}}\dfrac{2}{61}\Big{)}\]\[A_{N}=\left(\begin{array}{cccc}\frac{46268635184890481}{6231747944448000}&\\ -\frac{843924159892681}{239682613248000}&\frac{2095498352743}{2535104563200}& \frac{240331128931}{2535104563200}&-\frac{10279031063}{122060590080}\\ -4&\frac{3733202770769}{25351045632000}&-\frac{8883867896017}{6337761408000}& \frac{192302368031}{24412118016000}\\ \frac{39222471881369}{27696657530880}&-\frac{637146509711}{2816782848000}&- \frac{191242568381}{352097856000}&\frac{175009899277}{8137372672000}\\ \end{array}\right)\]  
\[K_{N}=\left(\begin{array}{cccc}\frac{95205971609617}{35952391987200}&\\ \frac{28298016708823}{167316901171200}&-\frac{1296366536717}{418292259280}&\\ -\frac{958020525197}{864240192000}&-\frac{2425439590003}{104573063232000}&- \frac{27877023310129}{41829225292800}&\\ -\frac{958020525197}{14980163328000}&-\frac{2425439590003}{69715375488000}& \frac{1296366536717}{69715375488000}&-\frac{22310489177}{4882423603200}\\ \end{array}\right)\]