/* PROGRAM coupled_oscillators */ /* n 個の質点からなる連成振動子の運動を */ /* 0 < t < TEND の範囲で解く。 */ /* 長さ 2*N の配列 w[0~(N-1)][0~1] を定義して, */ /* j 番目の質点の変位を w[j][0], */ /* 速度を w[j][1] に格納する。 */ /* 質点の質量の逆数に比例する無次元パラメータは */ /* 配列 c[0~(N-1)] に格納する。 */ /* 初期条件は変位ゼロ, */ /* 速度は 1 番目の質点のみ VZERO とする。 */ #include<stdio.h> #define N 10 #define VZERO 0.1 #define TEND 100.0 void rhs(double f[N][2], double w[N][2], double c[N], int n); int main(void){ int j; double t,dt, c[N], w[N][2],p[N][2], k1[N][2], k2[N][2], k3[N][2], k4[N][2]; /* 時間ステップの刻み幅 dt を標準入力から読み込む。*/ /* 質量はみんな同じ。*/ for(j=0;j<N;++j)c[j] = 1.0; /* 未知変数 w と時刻 t の初期化。*/ for(j=0;j<N;++j) w[j][0] = 0.0, w[j][1] = j==0 ? VZERO : 0.0; t = 0.0; /* 時間積分の開始(無限 for loop)。*/ for(;;){ /* 時刻 t での質点の位置を書き出す。*/ for(j=0;j<N;++j) /* 時刻が TEND を超えたら無限 for loop から脱出する。*/ if ( t >= TEND ) break; /* 4次ルンゲ・クッタ法。微分方程式を */ /* dw/dt = f(w) だと思って,機械的に */ /* アルゴリズムを適用する。*/ /* まず補助変数 k1 = f(p) を計算する。*/ for(j=0;j<N;++j) p[j][0]=w[j][0], p[j][1]=w[j][1]; rhs(k1, p, c, N); /* 補助変数 k2 = f(p) を計算する。*/ for(j=0;j<N;++j) p[j][0]=w[j][0] + 0.5*dt*k1[j][0], p[j][1]=w[j][1] + 0.5*dt*k1[j][1]; rhs(k2, p, c, N); /* 補助変数 k3 = f(p) を計算する。*/ for(j=0;j<N;++j) p[j][0]=w[j][0] + 0.5*dt*k2[j][0], p[j][1]=w[j][1] + 0.5*dt*k2[j][1]; rhs(k3, p, c, N); /* 補助変数 k4 = f(p) を計算する。*/ for(j=0;j<N;++j) p[j][0]=w[j][0] + dt*k3[j][0], p[j][1]=w[j][1] + dt*k3[j][1]; rhs(k4, p, c, N); /* 未知変数 w と時刻 t を次の時間ステップでの値で上書きする。*/ for(j=0;j<N;++j) w[j][0]=w[j][0] + (dt/6.0)*(k1[j][0]+k4[j][0]+2.0*(k2[j][0]+k3[j][0])), w[j][1]=w[j][1] + (dt/6.0)*(k1[j][1]+k4[j][1]+2.0*(k2[j][1]+k3[j][1])); t = t + dt; } return 0;} /* 微分方程式 dw/dt = f(w) の右辺を計算するサブルーチン。*/ void rhs(double f[N][2], double w[N][2], double c[N], int n){ int j; for(j=0;j<n;++j){ /* du(j)/dt = v(j) */ f[j][0] = w[j][1]; /* dv(j)/dt = -c(j) * (2u(j) - u(j-1) - u(j+1)) */ if ( j == 0 ) { f[j][1] = - c[j] * (2.0*w[j][0] - w[j+1][0]); } else if ( j == n-1 ) { f[j][1] = - c[j] * (2.0*w[j][0] - w[j-1][0]); } else { f[j][1] = - c[j] * (2.0*w[j][0] - w[j-1][0] - w[j+1][0]); } } }
1.0
0.0000000 9.09090909e-02 1.81818182e-01 2.72727273e-01 3.63636364e-01 4.54545455e-01 5.45454545e-01 6.36363636e-01 7.27272727e-01 8.18181818e-01 9.09090909e-01 1.0000000 1.57575758e-01 1.98484848e-01 2.72727273e-01 3.63636364e-01 4.54545455e-01 5.45454545e-01 6.36363636e-01 7.27272727e-01 8.18181818e-01 9.09090909e-01 2.0000000 1.29797980e-01 2.34595960e-01 2.89393939e-01 3.65025253e-01 4.54545455e-01 5.45454545e-01 6.36363636e-01 7.27272727e-01 8.18181818e-01 9.09090909e-01 3.0000000 8.32702020e-02 2.23918876e-01 3.20991162e-01 3.80418771e-01 4.56744529e-01 5.45541351e-01 6.36363636e-01 7.27272727e-01 8.18181818e-01 9.09090909e-01 4.0000000 8.03959736e-02 1.80786160e-01 3.16998106e-01 4.07994003e-01 4.71269992e-01 5.48319129e-01 6.36575828e-01 7.27277550e-01 8.18181818e-01 9.09090909e-01 5.0000000 9.33183470e-02 1.68123098e-01 2.76796685e-01 4.08329168e-01 4.96055389e-01 5.62066908e-01 6.39759301e-01 7.27629193e-01 8.18198898e-01 9.09091160e-01 6.0000000 9.40571654e-02 1.81667494e-01 2.57116640e-01 3.72471705e-01 4.98997183e-01 5.84695203e-01 6.52840600e-01 7.31105316e-01 8.18688937e-01 9.09127308e-01 7.0000000 9.03009539e-02 1.86505335e-01 2.69323877e-01 3.47865678e-01 4.67313478e-01 5.89331457e-01 6.73748514e-01 7.43604106e-01 8.22379606e-01 9.09745574e-01 8.0000000 9.01017895e-02 1.81923446e-01 2.78486018e-01 3.56732363e-01 4.39674553e-01 5.61435891e-01 6.79508572e-01 7.63098802e-01 8.34358203e-01 9.13506441e-01 9.0000000 9.09899746e-02 1.80471752e-01 2.74227014e-01 3.69374044e-01 4.44514621e-01 5.32121253e-01 6.54944873e-01 7.69607906e-01 8.52547145e-01 9.24178190e-01 10.0000000 9.11034189e-02 1.81770595e-01 2.70851267e-01 3.66928576e-01 4.59349802e-01 5.32864810e-01 6.24892131e-01 7.47792560e-01 8.58626433e-01 9.37417541e-01 11.0000000 9.09526447e-02 1.82128082e-01 2.72237983e-01 3.61705108e-01 4.59581913e-01 5.48644505e-01 6.21627355e-01 7.16633334e-01 8.35358717e-01 9.34061226e-01 12.0000000 9.08509028e-02 1.81878128e-01 2.73241242e-01 3.62416241e-01 4.53079403e-01 5.51676520e-01 6.36252682e-01 7.05983839e-01 7.95207224e-01 9.01451829e-01 13.0000000 9.08683643e-02 1.81766323e-01 2.72878824e-01 3.64179325e-01 4.52232651e-01 5.43544304e-01 6.38260428e-01 7.10850125e-01 7.70824029e-01 8.64579782e-01 14.0000000 9.09359180e-02 1.81757097e-01 2.72576736e-01 3.63693848e-01 4.53383428e-01 5.37055807e-01 6.21869113e-01 7.05352859e-01 7.76596342e-01 8.66080690e-01 15.0000000 9.09180808e-02 1.81763478e-01 2.72287482e-01 3.61827477e-01 4.49439944e-01 5.30179591e-01 6.04053307e-01 6.91859768e-01 7.99610684e-01 9.05388019e-01 16.0000000 9.08194674e-02 1.81434646e-01 2.70953483e-01 3.57599231e-01 4.39345203e-01 5.17913073e-01 5.98557936e-01 6.96929982e-01 8.21855229e-01 9.33835513e-01 17.0000000 9.04592518e-02 1.79938683e-01 2.66743062e-01 3.48646279e-01 4.26362349e-01 5.09074508e-01 6.09983226e-01 7.23984362e-01 8.32006289e-01 9.23373306e-01 18.0000000 8.90530413e-02 1.75708073e-01 2.57847323e-01 3.36237711e-01 4.18685761e-01 5.17187829e-01 6.33464257e-01 7.44766944e-01 8.26467685e-01 9.00780157e-01 19.0000000 8.52570944e-02 1.67162703e-01 2.45779540e-01 3.28367378e-01 4.26364047e-01 5.40758504e-01 6.51612358e-01 7.40015909e-01 8.14476433e-01 8.98470388e-01 20.0000000 7.83672758e-02 1.55920291e-01 2.38121370e-01 3.35167823e-01 4.48649639e-01 5.60445322e-01 6.49407229e-01 7.23467340e-01 8.10979343e-01 9.10324364e-01 21.0000000 7.11942141e-02 1.49810890e-01 2.44716820e-01 3.56681637e-01 4.68644163e-01 5.59686610e-01 6.34430202e-01 7.18092446e-01 8.17415456e-01 9.14700373e-01 22.0000000 7.16659021e-02 1.59448592e-01 2.66834184e-01 3.77551644e-01 4.69708754e-01 5.44815709e-01 6.27232729e-01 7.25712873e-01 8.22070465e-01 9.09704209e-01 23.0000000 8.73165907e-02 1.87022681e-01 2.91541587e-01 3.81669318e-01 4.56017529e-01 5.36311926e-01 6.33501635e-01 7.31752426e-01 8.19684632e-01 9.06606881e-01 24.0000000 1.13598681e-01 2.18183758e-01 3.03201806e-01 3.72281686e-01 4.47773537e-01 5.42168204e-01 6.40692188e-01 7.29512184e-01 8.16512680e-01 9.08404482e-01 25.0000000 1.30407365e-01 2.30732606e-01 3.00766867e-01 3.68903506e-01 4.55960057e-01 5.51735017e-01 6.40130115e-01 7.25766286e-01 8.17154253e-01 9.10073126e-01 26.0000000 1.19462967e-01 2.15518014e-01 2.96147996e-01 3.81722222e-01 4.71891981e-01 5.55722564e-01 6.37579921e-01 7.26611496e-01 8.19027358e-01 9.09565405e-01 27.0000000 8.81115688e-02 1.86306137e-01 2.94590500e-01 3.97723711e-01 4.82735335e-01 5.58584944e-01 6.41148654e-01 7.30423345e-01 8.19633251e-01 9.08982705e-01 28.0000000 6.65529141e-02 1.66072715e-01 2.87617809e-01 3.97255144e-01 4.85357428e-01 5.66925690e-01 6.50577612e-01 7.34762104e-01 8.20655470e-01 9.09723283e-01 29.0000000 7.42116237e-02 1.65700047e-01 2.70761338e-01 3.77674856e-01 4.80999430e-01 5.76175827e-01 6.60696335e-01 7.41025980e-01 8.24574675e-01 9.11653469e-01 30.0000000 9.66776740e-02 1.77926403e-01 2.56778304e-01 3.54939803e-01 4.68406047e-01 5.75323391e-01 6.66835933e-01 7.49943585e-01 8.31737962e-01 9.14972052e-01 31.0000000 1.05730631e-01 1.88440172e-01 2.60153690e-01 3.45977892e-01 4.50301548e-01 5.60533232e-01 6.64582579e-01 7.57057123e-01 8.40137131e-01 9.19954683e-01 32.0000000 9.52109375e-02 1.89210541e-01 2.75458624e-01 3.53836246e-01 4.38430806e-01 5.40341790e-01 6.51288694e-01 7.55022343e-01 8.45056929e-01 9.24838417e-01 33.0000000 8.36502475e-02 1.82921583e-01 2.83682632e-01 3.67473805e-01 4.42364414e-01 5.28605046e-01 6.31656400e-01 7.40145340e-01 8.39845262e-01 9.24958288e-01 34.0000000 8.50602518e-02 1.77816672e-01 2.77413199e-01 3.73212648e-01 4.56113570e-01 5.32192586e-01 6.17409622e-01 7.17286742e-01 8.20865242e-01 9.15418040e-01 35.0000000 9.28695490e-02 1.78662869e-01 2.67958032e-01 3.67484502e-01 4.63598866e-01 5.43842812e-01 6.16466132e-01 6.98096265e-01 7.93928242e-01 8.96836464e-01 36.0000000 9.49757433e-02 1.82542756e-01 2.67023305e-01 3.58662320e-01 4.57104032e-01 5.48411871e-01 6.23337782e-01 6.92082012e-01 7.74262511e-01 8.79187052e-01 37.0000000 9.10500340e-02 1.83779739e-01 2.71961851e-01 3.55521485e-01 4.44214360e-01 5.38320058e-01 6.24604982e-01 6.98482280e-01 7.76058975e-01 8.76817976e-01 38.0000000 8.83463886e-02 1.81100380e-01 2.72937773e-01 3.56485446e-01 4.35654118e-01 5.21409195e-01 6.15309009e-01 7.08713035e-01 7.99188256e-01 8.95024255e-01 39.0000000 8.90285702e-02 1.77443584e-01 2.66795234e-01 3.53493660e-01 4.32614520e-01 5.11904006e-01 6.06368921e-01 7.16986607e-01 8.27042076e-01 9.21014713e-01 40.0000000 8.90862958e-02 1.74236489e-01 2.58082629e-01 3.44110894e-01 4.30176749e-01 5.16219417e-01 6.12235538e-01 7.25012001e-01 8.40123903e-01 9.32941473e-01 41.0000000 8.58345981e-02 1.69679525e-01 2.50991098e-01 3.35151466e-01 4.28722431e-01 5.30045606e-01 6.32835368e-01 7.34550877e-01 8.32889577e-01 9.21692336e-01 42.0000000 8.08430060e-02 1.63087727e-01 2.46699645e-01 3.34927145e-01 4.34863749e-01 5.45686283e-01 6.52051493e-01 7.40169557e-01 8.16824840e-01 9.01331454e-01 43.0000000 7.71178578e-02 1.58235618e-01 2.47386138e-01 3.45616644e-01 4.50629273e-01 5.57115548e-01 6.54738906e-01 7.35238495e-01 8.07564910e-01 8.93615789e-01 44.0000000 7.73384565e-02 1.61221477e-01 2.57000496e-01 3.62765675e-01 4.67199146e-01 5.59831790e-01 6.42044012e-01 7.23410981e-01 8.10549063e-01 9.03665853e-01 45.0000000 8.40313619e-02 1.75474622e-01 2.75809249e-01 3.78661186e-01 4.72850778e-01 5.52744686e-01 6.28487056e-01 7.17075110e-01 8.19066390e-01 9.16464447e-01 46.0000000 9.76857701e-02 1.97910756e-01 2.96597543e-01 3.86352705e-01 4.65685906e-01 5.42167315e-01 6.26326622e-01 7.22512765e-01 8.23719022e-01 9.17351221e-01 47.0000000 1.13277597e-01 2.18460951e-01 3.08861635e-01 3.84399138e-01 4.56140561e-01 5.38898938e-01 6.35000022e-01 7.32184298e-01 8.21711261e-01 9.08867333e-01 48.0000000 1.20778752e-01 2.24710791e-01 3.07260455e-01 3.79073894e-01 4.56612412e-01 5.47702801e-01 6.44913357e-01 7.35271242e-01 8.17539056e-01 9.03720479e-01 49.0000000 1.12420721e-01 2.10864448e-01 2.95548518e-01 3.78842373e-01 4.69197610e-01 5.61943277e-01 6.49036783e-01 7.31626501e-01 8.16782125e-01 9.07085958e-01 50.0000000 9.13881385e-02 1.84423810e-01 2.82180486e-01 3.84477625e-01 4.83695336e-01 5.71217774e-01 6.49336726e-01 7.30400400e-01 8.20646431e-01 9.12762100e-01 51.0000000 7.23154020e-02 1.62595401e-01 2.72652903e-01 3.86736198e-01 4.87372047e-01 5.72099252e-01 6.52157056e-01 7.37128160e-01 8.26359974e-01 9.14571207e-01 52.0000000 6.99240323e-02 1.59067772e-01 2.66886598e-01 3.76745143e-01 4.76431791e-01 5.68339816e-01 6.58936004e-01 7.47496523e-01 8.31380014e-01 9.14218173e-01 53.0000000 8.49218555e-02 1.72667450e-01 2.63520752e-01 3.58010073e-01 4.58218238e-01 5.62598475e-01 6.63355545e-01 7.53671877e-01 8.35463955e-01 9.16301464e-01 54.0000000 1.02258387e-01 1.89197020e-01 2.64034829e-01 3.44926348e-01 4.43670934e-01 5.53139383e-01 6.58027575e-01 7.51938338e-01 8.38294599e-01 9.20543630e-01 55.0000000 1.05767157e-01 1.94887786e-01 2.70138772e-01 3.48085771e-01 4.39058324e-01 5.39838479e-01 6.42663469e-01 7.42725783e-01 8.36767057e-01 9.22005060e-01 56.0000000 9.45093673e-02 1.88065526e-01 2.78318455e-01 3.62872679e-01 4.43796235e-01 5.29004711e-01 6.24792142e-01 7.27460874e-01 8.26733605e-01 9.16739994e-01 57.0000000 8.24679724e-02 1.78107579e-01 2.81035620e-01 3.74326814e-01 4.52686728e-01 5.28012061e-01 6.13257229e-01 7.09119567e-01 8.08162932e-01 9.05158291e-01 58.0000000 8.19761999e-02 1.74485655e-01 2.75127614e-01 3.72381473e-01 4.58635083e-01 5.35783505e-01 6.11574497e-01 6.94217158e-01 7.88068336e-01 8.91626009e-01 59.0000000 9.06324433e-02 1.78066255e-01 2.66347680e-01 3.60478943e-01 4.55944002e-01 5.42038628e-01 6.16340267e-01 6.90111605e-01 7.77469940e-01 8.82919935e-01 60.0000000 9.65033380e-02 1.82461974e-01 2.62701854e-01 3.49506829e-01 4.44604913e-01 5.37628984e-01 6.20779945e-01 6.98739632e-01 7.84037389e-01 8.85448336e-01 61.0000000 9.32586612e-02 1.81803557e-01 2.64585601e-01 3.45695631e-01 4.31509098e-01 5.24573996e-01 6.20708246e-01 7.14267536e-01 8.05646366e-01 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