APPLICATION OF QUASILINEARIZATION TO THE SOLUTION OF NON-LINEAR DIFFERENTIAL EQUATIONS.
KANSAS STATE UNIV MANHATTAN
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This report introduces the reader to the use of the quasilinearization technique which was developed by Bellman and Kalaba and applied extensively to chemical engineering problems by Lee in obtaining numerical solutions of certain classes of nonlinear ordinary differential equations of the boundary value type encountered in chemical engineering, optimization, the boundary layer theory, and in control problems. The nonlinear differential equation is first represented by a set of simultaneous first order differential equations. Each of the first order nonlinear differential equations is linearized using the Taylor series expansion with second and higher order terms omitted. Iterative solution of the resulting linear differential equations usually converges quadratically to the solution of the original equation. This means that each iteration approximately doubles the number of digits of accuracy. A simple problem of steady flow in the boundary layer along a cylinder near the forward stagnation point is solved to illustrate the use of the technique.
- Numerical Mathematics
- Fluid Mechanics