Application of Spline Collocation to Partial Differential Equations. Spline Collocation for Partial Differential Equations

      Аннотация: The study of differential equations is an extensive field in pure and applied Mathematics. differential equations play an important role in every physical or technical process. Differential equations like those wont to solve real-life issues might not be solvable analytically or terribly tough to possess closed-form solutions are often approximated by numerical methods. During the last few years, piecewise polynomial approximations have become very important in engineering applications. The most popular of such approximating functions are spline functions. The various features of the Spline collocation technique enhance the applicability in the field of numerical analysis to partial differential equations. The present work deals with the use of Spline collocation method to various types of linear as well as non-linear Partial Differential Equations (PDEs) under the different set of boundary conditions. LinearPDEs are solved using Spline explicit and implicit schemes while non-linear PDEs are handled withHofp-Cole transformation and Orlowski and Soczyk transformation (OST) to apply Spline collocation method.

Ключевые слова: Partial Differential Equations, Hofp-Cole Transformation, Burgers equations, Navier-Stokes equations, Spline collocation Method, OST Transformation