Solve a Volterra Integral Equation
Solve a Volterra integral equation using DSolveValue.
In[1]:=
eqn = y[x] == x^3 + \[Lambda] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(x\)]\(\((t - \ x)\) y[
t] \[DifferentialD]t\)\);
In[2]:=
sol = DSolveValue[eqn, y[x], x]
Out[2]=
Plot the solution for different values of λ.
In[3]:=
Plot[Table[sol, {\[Lambda], 1, 3, 0.5}] // Evaluate, {x, 0, 20}]
Out[3]=
Solve a weakly singular Volterra integral equation.
In[4]:=
eqn = y[x] == x^a - \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(x\)]\(
\*FractionBox[\(y[t]\),
SqrtBox[\(x - t\)]] \[DifferentialD]t\)\);
Use DSolveValue to obtain an expression for the solution.
In[5]:=
sol = DSolveValue[eqn, y[x], x]
Out[5]=
Plot the solution.
In[6]:=
Plot[Table[sol, {a, 1, 4, 0.7}] // Evaluate, {x, 0, 2}]
Out[6]=