Iterative Method for a System of Nonlinear Fredholm Integral Equations

Algorithm 1

: Iteration algorithm.

(i)	Step 1. Choose and calculate () along with . Moreover, given the value of and the initial vectors , set .
(ii)	Step 2. Solve the nonlinear system where and .
(iii)	Step 3. In Algorithm 1, using the composite trapezoidal rule or using the composite Simpson rule where and , .
(iv)	Step 4. Calculate the Jacobian matrix .
(v)	Step 5. Calculate [; ] by steps 2–4.
(vi)	Step 6. Compute . If , stop; otherwise, set and go to step 5.
Next, we can derive the following convergence result for the iteration method.