求解弗雷德霍姆 (Fredholm) 积分方程

用 DSolveValue 解一个弗雷德霍姆积分方程

In[1]:=

eqn = y[x] == Sin[7 x] - x/a + \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), FractionBox[\(\[Pi]\), \(2\)]]\(\(x\ y[t]\) \[DifferentialD]t\)\);

In[2]:=

sol = DSolveValue[eqn, y[x], x]

Out[2]=

绘制解的曲线.

In[3]:=

Plot[Table[sol, {a, -1, 4, 0.7}] // Evaluate, {x, 0, Pi/2}]

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解一个第二类齐次弗雷德霍姆方程.

In[4]:=

eqn = y[x] == \[Lambda] \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(Cos[x + t] y[ t] \[DifferentialD]t\)\);

In[5]:=

sol = DSolveValue[eqn, y[x], x]

Out[5]=

绘制解的曲线.

In[6]:=

Plot[Table[ sol /. {C[1] -> 1, C[2] -> 1}, {\[Lambda], {-2/Pi, 2/Pi}}] // Evaluate, {x, 0, 3 \[Pi]}]

Out[6]=