Coefficients for rosenbrock methods corrected

AMDiS/src/time/RosenbrockMethod.cc

@@ -47,21 +47,21 @@ namespace AMDiS {
 
     createData();
     
-    // b1(2) = 0.5
-    // b1(1) = 1-b1(2) = 0.5
-    // alpha(2,1) = 1/(2*b1(2)) = 1
+    // b(2) = 0.5
+    // b(1) = 1-b(2) = 0.5
+    // alpha(2,1) = 1/(2*b(2)) = 1
     // gamma = 1+1/sqrt(2) = 1.707...
-    // gamma(2,1) = -gamma/b1(2) = -3.41421356237309
-    // b2(1) = 1
-    // b2(2) = 0
+    // gamma(2,1) = -gamma/b(2) = -3.41421356237309
+    // b_(1) = 1
+    // b_(2) = 0
 
     a[0][0] = 0.0;
     a[1][0] = 5.857864376269050e-01;
-    a[1][1] = a[1][0];
+    a[1][1] = 1.0;
 
     c[0][0] = gamma;
     c[1][0] = -1.171572875253810e+00;
-    c[1][1] = c[1][0] + gamma;
+    c[1][1] = -gamma;
 
     m1[0] = 8.786796564403575e-01;
     m1[1] = 2.928932188134525e-01;
@@ -87,11 +87,11 @@ namespace AMDiS {
     a[2][0] = 1.605996252195329e+00;
     a[2][2] = 0.7;
     
-    c[0][0] =  0.435866521508459;
-    c[1][0] = 8.874044410657833e-01;
+    c[0][0] =  gamma;
+    c[1][0] =  8.874044410657833e-01;
     c[1][1] =  0.604455284065559;
-    c[2][0] = 2.398747971635036e+01;
-    c[2][1] = 5.263722371562129e+00;
+    c[2][0] =  2.398747971635036e+01;
+    c[2][1] =  5.263722371562129e+00;
     c[2][2] =  6.37978879934488;
     
     m1[0] =  2.236727045296590e+00;
@@ -114,26 +114,26 @@ namespace AMDiS {
     createData();
     
     a[0][0] = 0.0;
-    a[1][0] = 1.26794919243112;
+    a[1][0] = 1.267949192431123;
     a[1][1] = 1.0;
-    a[2][0] = 1.26794919243112;
+    a[2][0] = 1.267949192431123;
     a[2][1] = 0.0;
     a[2][2] = 1.0;
     
-    c[0][0] =  0.788675134594813;
-    c[1][0] = -1.60769515458674;
-    c[1][1] = -0.211324865405187;
-    c[2][0] = -3.46410161513775;
-    c[2][1] = -1.73205080756888;
-    c[2][2] = -1.07735026918963;
+    c[0][0] =  gamma;
+    c[1][0] = -1.607695154586736;
+    c[1][1] = -0.2113248654051871;
+    c[2][0] = -3.464101615137755;
+    c[2][1] = -1.732050807568877;
+    c[2][2] = -1.077350269189626;
     
     m1[0] = 2.0;
-    m1[1] = 0.577350269189625;
-    m1[2] = 0.422649730810374;
+    m1[1] = 0.5773502691896258;
+    m1[2] = 0.4226497308103742;
     
-    m2[0] = 2.11324865405187;
+    m2[0] = 2.113248654051871;
     m2[1] = 1.0;
-    m2[2] = 0.422649730810374;
+    m2[2] = 0.4226497308103742;
 	
     MSG("Rosenbrock scheme Ros3p\n");
   }
@@ -143,26 +143,25 @@ namespace AMDiS {
   {
     order = 4;
     stages = 6;
-    gamma = 2.5e-01;
+    gamma = 0.25;
 
     createData();
 
     a[0][0] = 0.0;
-    
     a[1][0] =  3.0;
-//     a[1][1] = 
+    a[1][1] =  0.75;
     a[2][0] =  1.831036793486759e+00;
     a[2][1] =  4.955183967433795e-01;
-//     a[2][2] = 
+    a[2][2] =  0.21;
     a[3][0] =  2.304376582692669e+00;
     a[3][1] = -5.249275245743001e-02;
     a[3][2] = -1.176798761832782e+00;
-//     a[3][3] = 
+    a[3][3] =  0.63;
     a[4][0] = -7.170454962423025e+00;
     a[4][1] = -4.741636671481786e+00;
     a[4][2] = -1.631002631330971e+01;
     a[4][3] = -1.062004044111401e+00;
-//     a[4][4] = 
+    a[4][4] =  1.0;
     a[5][0] = -7.170454962423025e+00;
     a[5][1] = -4.741636671481785e+00;
     a[5][2] = -1.631002631330971e+01;
@@ -171,27 +170,26 @@ namespace AMDiS {
     a[5][5] =  1.0;
 
     c[0][0] =  gamma;
-    
     c[1][0] = -1.200000000000000e+01;
-//     c[1][1] =  4.0;
+    c[1][1] = -0.5;
     c[2][0] = -8.791795173947035e+00;
     c[2][1] = -2.207865586973518e+00;
-//     c[2][2] =  4.0;
+    c[2][2] = -0.023504;
     c[3][0] =  1.081793056857153e+01;
     c[3][1] =  6.780270611428266e+00;
     c[3][2] =  1.953485944642410e+01;
-//     c[3][3] =  4.0;
+    c[3][3] = -0.0362;
     c[4][0] =  3.419095006749677e+01;
     c[4][1] =  1.549671153725963e+01;
     c[4][2] =  5.474760875964130e+01;
     c[4][3] =  1.416005392148534e+01;
-//     c[4][4] =  4.0;
+    c[4][4] =  0.0;
     c[5][0] =  3.462605830930533e+01;
     c[5][1] =  1.530084976114473e+01;
     c[5][2] =  5.699955578662667e+01;
     c[5][3] =  1.840807009793095e+01;
     c[5][4] = -5.714285714285717e+00;
-//     c[5][5] =  4.0;
+    c[5][5] =  0.0;
 
     m1[0] = -7.170454962423026e+00;
     m1[1] = -4.741636671481786e+00;
@@ -206,7 +204,6 @@ namespace AMDiS {
     m2[3] = -1.062004044111401e+00;
     m2[4] =  1.0;
 	
-    WARNING("You have to fill the diagonals of the coeffcients to use time derivatives of your operators!\n");
     MSG("Rosenbrock scheme Rodasp\n");
   }
 
@@ -220,34 +217,34 @@ namespace AMDiS {
     createData();
 
     a[0][0] =  0.0;
-    a[1][0] =  1.14714018013952;
+    a[1][0] =  1.147140180139521;
     a[1][1] =  0.5;
-    a[2][0] =  1.32930341703716;
+    a[2][0] =  1.785764587181959;
     a[2][1] =  0.442124760965983;
     a[2][2] =  0.75;
-    a[3][0] = -2.19977665049954;
-    a[3][1] =  4.55821087656518;
-    a[3][2] = -1.37361554490645;
+    a[3][0] =  2.506239510951673;
+    a[3][1] =  4.558210876565182;
+    a[3][2] = -1.373615544906449;
     a[3][3] =  1.0;
 
     c[0][0] =  gamma;
-    c[1][0] = -0.263186118578107;
-    c[1][1] =  0.385866521508459;
-    c[2][0] = -3.35635061779949;
+    c[1][0] = -2.631861185781065;
+    c[1][1] = -0.064133478491541;
+    c[2][0] = -3.011310475541004;
     c[2][1] =  0.334203214637756;
     c[2][2] = -0.145563307177156;
-    c[3][0] = -2.6183067448488;
-    c[3][1] = -1.08994123815716;
-    c[3][2] = -1.71836543021444;
+    c[3][0] = -3.743590594301783;
+    c[3][1] = -1.089941238157158;
+    c[3][2] = -1.718365430214442;
     c[3][3] = -0.135847884055848;
     
-    m1[0] = -1.24823690752574;
-    m1[1] =  3.9534178869996;
-    m1[2] = -1.21522771421847;
-    m1[3] =  1.16541744745931;
+    m1[0] =  2.833375148827832;
+    m1[1] =  3.953417886999603;
+    m1[2] = -1.215227714218472;
+    m1[3] =  1.165417447459307;
 
-    m2[0] =  0.919998349829964;
-    m2[1] =  1.77038079363523;
+    m2[0] =  2.747785798103605;
+    m2[1] =  1.770380793635233;
     m2[2] =  0.257316038155499;
     m2[3] =  0.343556220548095;
 	
@@ -264,36 +261,36 @@ namespace AMDiS {
     createData();
 
     a[0][0] =  0.0;
-    a[1][0] =  1.14714018013952;
+    a[1][0] =  1.147140180139521;
     a[1][1] =  0.5;
-    a[2][0] = -0.79265181178863;
-    a[2][1] =  3.48693217206767;
+    a[2][0] =  2.807348188211369;
+    a[2][1] =  3.486932172067671;
     a[2][2] =  1.0;
-    a[3][0] = -0.79265181178863;
-    a[3][1] =  3.48693217206767;
+    a[3][0] =  a[2][0];
+    a[3][1] =  a[2][1];
     a[3][2] =  0.0;
     a[3][3] =  1.0;
 
     c[0][0] =  gamma;
-    c[1][0] = -0.263186118578107;
-    c[1][1] =  0.385866521508459;
-    c[2][0] = -1.40507848232679;
-    c[2][1] =  6.18104102134041;
-    c[2][2] =  1.20849664917601;
-    c[3][0] =  4.99718323859189;
-    c[3][1] = -6.54597265243973;
+    c[1][0] = -2.631861185781065;
+    c[1][1] = -0.064133478491541;
+    c[2][0] =  4.976389977276388;
+    c[2][1] =  6.181041021340408;
+    c[2][2] =  1.208496649176010;
+    c[3][0] = -1.761050184345382;
+    c[3][1] = -6.545972652439727;
     c[3][2] = -0.539706236424999;
     c[3][3] =  0.0;
     
-    m1[0] = -0.792651811788631;
-    m1[1] =  3.48693217206767;
+    m1[0] =  2.807348188211369;
+    m1[1] =  3.486932172067672;
     m1[2] =  0.0;
     m1[3] =  1.0;
 
-    m2[0] =  6.55610198824936;
-    m2[1] = -5.94329934171132;
+    m2[0] =  0.420084258522926;
+    m2[1] = -5.943299341711317;
     m2[2] =  0.360559439940373;
-    m2[3] = -3.34373891242489;
+    m2[3] = -3.343738912424890;
 	
     MSG("Rosenbrock scheme ROSI2P2\n");
   }
@@ -319,7 +316,7 @@ namespace AMDiS {
 	
     c[0][0] = gamma;
     c[1][0] = -4.58856072055827;
-    c[1][1] = -0.435866521508468;
+    c[1][1] = -gamma;
     c[2][0] = -4.56739138878308;
     c[2][1] = -0.0683107605436897;
     c[2][2] = -0.418867127163069;
@@ -363,7 +360,7 @@ namespace AMDiS {
 
     c[0][0] = gamma;
     c[1][0] = -4.58856072055827;
-    c[1][1] = -0.435866521508468;
+    c[1][1] = -gamma;
     c[2][0] =  48.3965596116246;
     c[2][1] =  16.132186537208;
     c[2][2] =  6.56544000523295;
@@ -404,9 +401,9 @@ namespace AMDiS {
     a[2][1] = 0.0;
     a[2][2] = 0.5;
 
-    c[0][0] =  0.788675134594813;
+    c[0][0] =  gamma;
     c[1][0] = -2.53589838486225;
-    c[1][1] = -0.788675134594813;
+    c[1][1] = -gamma;
     c[2][0] = -1.62740473580836;
     c[2][1] = -0.274519052838329;
     c[2][2] = -0.0528312163512967;
@@ -446,9 +443,9 @@ namespace AMDiS {
     a[3][2] =  2.29428036027904;
     a[3][3] =  1.0;
 	
-    c[0][0] =  0.435866521508459;
+    c[0][0] =  gamma;
     c[1][0] = -4.58856072055809;
-    c[1][1] = -0.435866521508459;
+    c[1][1] = -gamma;
     c[2][0] = -4.18476048231916;
     c[2][1] =  0.285192017355496;
     c[2][2] = -0.413333376233886;