A generalized Newton-Raphson method for nonlinear partial differential equations—packed-bed reactors with axial mixing

Abstract The generalized Newton-Raphson method, also known as the quasilinearization technique, is used to solve nonlinear differential equations of the boundary value type resulting from the transient equations of packed-bed reactors. This technique has been shown to be an effective tool for the numerical solution of boundary value problems in nonlinear ordinary differential equations. It is shown that this technique is equally effective in treating nonlinear parabolic partical differential equations. In one numerical example, only a few iterations are needed by this technique as compared to the 25 iterations required by the first-order convergent method ordinarily used.