Open Access2nd Order Parallel Splitting Methods for Heat Equation
Author(s) -
Muhammad Aziz,
M. A. Rehman
Publication year - 2017
Publication title -
scientific inquiry and review
Language(s) - English
Resource type - Journals
eISSN - 2521-2435
pISSN - 2521-2427
DOI - 10.32350/sir/11/010101
Subject(s) - mathematics , matrix exponential , boundary value problem , exponential function , heat equation , order (exchange) , mathematical analysis , boundary (topology) , matrix (chemical analysis) , derivative (finance) , function (biology) , differential equation , materials science , finance , evolutionary biology , financial economics , economics , composite material , biology
In this paper, heat equation in two dimensions with non local boundary condition is solved numerically by 2nd order parallel splitting technique. This technique used to approximate spatial derivative and a matrix exponential function is replaced by a rational approximation. Simpson’s 1/3 rule is also used to approximate the non local boundary condition. The results of numerical experiments are checked and compared with the exact solution, as well as with the results already existed in the literature and found to be highly accurate.