We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh–Schrödinger perturbation theory and termed iterative perturbative (IPT). Contrary to standard algorithms, which are either “direct” (to compute all eigenpairs) or “iterative” just few), IPT computes any number of eigenpairs with the same basic procedure. Thanks this perfect parallelism, proves more efficie...

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...