Title :
Two-Stage Sand-Runge-Kutta Methods Powerful for Non-linear Equations with Multiple Solutions
Author_Institution :
Shizuoka Inst. of Sci. & Technol., Shizuoka, Japan
Abstract :
A system of non-linear equations with multiple solutions is often appearing in field of science and technology. To solve efficiently such a system, the Runge-Kutta method is applied to an initial value problem of ordinary differential equations equivalent to its system. Then a class of iteration methods having third-order convergence for a simple solution is constructed. In addition, it is shown that there is a method possessing second-order convergence for a solution with any multiplicity in this class.
Keywords :
differential equations; initial value problems; iterative methods; nonlinear equations; Sand-Runge-Kutta methods; initial value problem; iteration methods; multiple solutions; nonlinear equations; ordinary differential equations; Concrete; Convergence of numerical methods; Differential equations; Jacobian matrices; Newton method; Nonlinear equations; Optimization methods; algebraic equations; high order convergence; multiple solutions; nonlinear equations;
Conference_Titel :
Future Computing, Service Computation, Cognitive, Adaptive, Content, Patterns, 2009. COMPUTATIONWORLD '09. Computation World:
Conference_Location :
Athens
Print_ISBN :
978-1-4244-5166-1
Electronic_ISBN :
978-0-7695-3862-4
DOI :
10.1109/ComputationWorld.2009.40
