A Two-Point Off-Grid Colocation Point for the Direct Solution of Fourth Order Ordinary Differential Equations

The desire to find solutions to differential equations cannot be over emphasized based on the importance of such equations. Many people have developed different initial value solvers to handle various differential equations based on the order of the differential equations. In solving differential equations of order greater than one, it is often the practiced to resolve such a differential equation into system of first order ordinary differential equations and then an appropriate method is applied. Also, in some cases the analytical solutions to some of the differential equations are intractable, hence there is need to circumvent this hurdle, and this is done by the introduction of approximate solution otherwise referred to as Numerical solution. This presentation focuses on derivation and implementation of a direct method to solve directly the fourth order ordinary differential equations by interpolating at some selected grid points and collocating at both grid and off grid points. Also, the derived method shall be applied to solve some fourth order ordinary differential equations to compare the level of accuracy of the method with the analytical solution.