ABSTRACT
When an ordinary differential equation involves boundary conditions instead of initial conditions, then a numerical approach is most often used to solve the problem. In a boundary value problem, we essentially need to fit a solution into the known boundary conditions as opposed to simply integrating from the initial conditions. To numerically solve a boundary value problem involving an ordinary, linear, and differential equation, we will need the difference formulas obtained by Taylor series expansion using just a few terms. The finite difference method first involves subdividing the independent variable domain into N subdivisions. First-order forward difference formula. Usually used for a y' boundary condition at the beginning of domain. First-order backward difference formula. Usually used for a y' boundary condition at end of the domain. Second-order central difference formula for the second derivative in the interior of the domain.
