Families of two-step fourth order P-stable methods for second oder differential equations
Journal of Computational and Applied Mathematics
Convergence and stability of boundary value methods for ordinary differential equations
Proceedings of the 6th international congress on Computational and applied mathematics
A conditionally P-stable fourth-order exponential-fitting method for y'' = f(f, y)
Journal of Computational and Applied Mathematics
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
On the A-stable methods in the GBDF class
Nonlinear Analysis: Real World Applications
B-Spline Linear Multistep Methods and their Continuous Extensions
SIAM Journal on Numerical Analysis
P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems
Computers & Mathematics with Applications
P-stable symmetric super-implicitmethods for periodic initial value problems
Computers & Mathematics with Applications
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In this paper, we introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. We rigorously prove that these schemes are P-stable, in a generalized sense, of arbitrarily high order. This overcomes the barrier that Lambert and Watson established in Lambert and Watson (1976) [1] on Linear Multistep Methods used in the classic way; that is as Initial Value Methods. We call the new methods PGSCMs, an acronym for P"@n-stable Generalized Stormer-Cowell Methods. Numerical illustrations which confirm the theoretical results of the paper are finally given.