Comparative study of some spectral based methods for solving boundary layer flow problems

System of highly nonlinear differential equations arising in modelling of fluid flow problems necessitated the researcher to continually develop efficient numerical methods having the capability to yield accurate solution. Over the years, various numerical schemes have been developed to tackle such problems. This paper provides a comparative study of three of such numerical algorithms i.e spectral quasilinearization method, spectral local linearization method and spectral relaxation method in terms of speed of convergence and accuracy. All of three methods are capable to figure out system of nonlinear differential equations. Study on the effect of their linearization approach, convergence and accuracy is important. To analyze this, the methods are applied on a number of differential equations modeling fluid flow of engineering interest and their linearization schemes are discussed in detail. The infinity norm of solution error between successive iterations is computed which measures the speed of convergence. Accuracy is compared by evaluating maximum residual error norm which is obtained by substituting approximate solution at each iteration into original equations. The obtained results show that the spectral local linearization method converges quickly than spectral quasilinearization method and it gives solution with optimum accuracy.