Open AccessAn Implicit Method for Numerical Solution of Singular and Stiff Initial Value Problems
Author(s) -
M. Kamrul Hasan,
M. Suzan Ahamed,
Mohammad Shamsul Alam,
Md. Anwer Hossain
Publication year - 2013
Publication title -
journal of computational engineering
Language(s) - English
Resource type - Journals
eISSN - 2356-7260
pISSN - 2314-6443
DOI - 10.1155/2013/720812
Subject(s) - runge–kutta methods , explicit and implicit methods , mathematics , diagonal , numerical methods for ordinary differential equations , singular solution , initial value problem , simple (philosophy) , euler's formula , midpoint method , singular value , mathematical analysis , numerical analysis , differential equation , ordinary differential equation , geometry , philosophy , eigenvalues and eigenvectors , physics , exact differential equation , epistemology , collocation method , quantum mechanics
An implicit method has been presented for solving singular initial value problems. The method is simple and gives more accurate solution than the implicit Euler method as well as the second order implicit Runge-Kutta (RK2) (i.e., implicit midpoint rule) method for some particular singular problems. Diagonally implicit Runge-Kutta (DIRK) method is suitable for solving stiff problems. But, the derivation as well as utilization of this method is laborious. Sometimes it gives almost similar solution to the two-stage third order diagonally implicit Runge-Kutta (DIRK3) method and the five-stage fifth order diagonally implicit Runge-Kutta (DIRK5) method. The advantage of the present method is that it is used with less computational effort
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