摘要：In this piece of work using only three grid points, we propose two sets of numerical methods in a coupled manner for the solution of fourth-order ordinary differential equation 𝑢𝑖𝑣(𝑥)=𝑓(𝑥,𝑢(𝑥),𝑢(𝑥),𝑢(𝑥),𝑢(𝑥)), 𝑎<𝑥<𝑏, subject to boundary conditions 𝑢(𝑎)=𝐴0, 𝑢(𝑎)=𝐴1, 𝑢(𝑏)=𝐵0, and 𝑢(𝑏)=𝐵1, where 𝐴0, 𝐴1, 𝐵0, and 𝐵1 are real constants. We do not require to discretize the boundary conditions. The derivative of the solution is obtained as a byproduct of the discretization procedure. We use block iterative method and tridiagonal solver to obtain the solution in both cases. Convergence analysis is discussed and numerical results are provided to show the accuracy and usefulness of the proposed methods.
