Implicit High-Order Numerical Method to Solve Integral Algebraic Equations in Case of Stiff Problem

Except in cases when the step size is assumed to be very small, several numerical techniques for solving the stiff equation are numerically unstable. Here, we explore numerical solution of integral algebraic equations (IAEs) in case of stiff problem. The implicit multistep collocation method uses the approximated values of the solution in the r previous steps and m collocation points in the current subinterval and the same number of collocation points in the next subinterval to calculate the approximate solution of the IAEs in the current subinterval. In order to validate theoretical developments in actual application, three examples have been thoroughly explored. Additionally, we solve IAEs using one-step and multistep collocation techniques, comparing numerical finding to demonstrate the effectiveness and high precision of the suggested approach.