Yasin Heydarpour

A novel multistep method based on the nonuniform rational basis spline curves is developed for the solution of a system of nonlinear differential equations. Efficiency of the presented method in terms of convergence and accuracy is demonstrated through the two-dimensional nonlinear transient heat transfer analysis of multilayered functionally graded truncated cone subjected to an internal thermal load with radiative–convective boundary condition at outer surface. In order to discretize the governing equations in the spatial domain, a layerwise-differential quadrature method is implemented. This transforms the partial differential equations into a system of nonlinear ordinary differential equations in the temporal domain, which is then solved using the presented technique. Comparative studies between predictions of the presented multistep technique and various existing numerical methods demonstrate superior computational efficiency of the method with low computational cost. High efficiency of this method indicated that the presented multistep approach can be successfully employed in various nonlinear problems. Finally, the effects of different parameters on the transient temperature of the truncated cone are studied. It is expected that the presented multistep method will be applied on various practical engineering problems in future studies.