Taylor series solution for a third order boundary value problem arising in Architectural Engineering

Many architectural systems are modelled by boundary value problems. Though there are many numerical and analytical methods to solve such problems, this paper suggests a simple but effective way to the third-order ordinary differential equations by the Taylor series technology. The governing equation is differentiated to obtain high order derivatives of a certain point, and solution is expanded into a Taylor series of the point, the boundary conditions are then used to identify the unknowns involved in the approximate solution. An example is given to elucidate the solution process, the maximal error is less 2%, and its accuracy can be further improved if a higher order series is solved. The approximate solution is compared with that by the variational iteration method, showing the present method is simpler and more straightforward. The comparison with the numerical solution culminates in its reliability and effectiveness. The method can be extended to fractal calculus.