ExDeqs.htm

(* 放物型偏微分方程式の練習&nbsp;&nbsp;&nbsp;2005/10/24&nbsp;&nbsp;aito *)

(* 場合1 初期分布が正弦波状 *)

f0[x_] := Sin[x * Pi]/;0&lt;=x <= 1

Plot[f0[x], {x, 0, 1}]

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deq0 = D[u[x, t], t] == D[u[x, t], {x, 2}] ;

cond1 = u[x, 0] == f0[x] ;

cond2 = u[0, t] == 0 ;

cond3 = u[1, t] == 0 ;

solution0 = NDSolve[{deq0, cond1, cond2, cond3}, u, {x, 0, 1}, {t, 0, 0.5}] ;

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(* 場合2 : 初期分布が直線 *)

f1[x_] := x/;0&lt;=x <= 0.5

f1[x_] := 1 - x/;0.5&lt;x <= 1

Plot[f1[x], {x, 0, 1}]

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deq1 = D[u[x, t], t] == D[u[x, t], {x, 2}] ;

cond1 = u[x, 0] == f1[x] ;

cond2 = u[0, t] == 0 ;

cond3 = u[1, t] == 0 ;

solution1 = NDSolve[{deq1, cond1, cond2, cond3}, u, {x, 0, 1}, {t, 0, 0.5}] ;

NDSolve :: mxsst : MaxPointsまたはMinStepSizeオプションで独立変数xに対して許容される最大グリッド点数10000が使用されます．  詳細

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