Tchebychev Polynomial Approximations for mthm^{th} Order Boundary Value Problems

Higher order boundary value problems (BVPs) play an important role modeling various scientific and engineering problems. In this article we develop an efficient numerical scheme for linear $m^{th}$ order BVPs. First we convert the higher order BVP to a first order BVP. Then we use Tchebychev orthogonal polynomials to approximate the solution of the BVP as a weighted sum of polynomials. We collocate at Tchebychev clustered grid points to generate a system of equations to approximate the weights for the polynomials. The excellency of the numerical scheme is illustrated through some examples.Comment: 21 pages, 10 figure

Evidence of Ferrimagnetism in Ferromagnetic La0_{67}Ca0_{33}MnO_3 nanoparticle

The present report is dedicated to show that ferromagnetic La0.67Ca0.33MnO3 (LCMN) particles can be better described in the framework of ferrimagnetic model. To confirm the ferrimagnetic signature in ferromagnetic LCMN particles, the temperature dependence of the inverse of magnetic susceptibility in the paramagnetic state of the samples was taken as a tool of data analysis. The observed ferrimagnetism is understood as an effect of of the core-shell spin structure in LCMN particles.Comment: 4 figure