scholarly journals High-order nonlinear initial-value problems countably determined

2009 ◽  
Vol 228 (1) ◽  
pp. 77-82 ◽  
Author(s):  
D. Gámez ◽  
A.I. Garralda Guillem ◽  
M. Ruiz Galán
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value

scholarly journals New explicit high‐order one‐step methods for singular initial value problems

2020 ◽  
Author(s):  
Bohdan Datsko ◽  
Myroslaw Kutniv ◽  
Andriy Kunynets ◽  
Andrzej Włoch
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value ◽  
One Step

scholarly journals High order linear initial-value problems and Schauder bases

2007 ◽  
Vol 31 (12) ◽  
pp. 2629-2638 ◽  
Author(s):  
E. Castro ◽  
D. Gámez ◽  
A.I. Garralda Guillem ◽  
M. Ruiz Galán
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value ◽  
Order Linear ◽  
Schauder Bases

scholarly journals Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity

2018 ◽  
Vol 7 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Tarek Saanouni
Keyword(s):  
Initial Value Problems ◽  
Evolution Equations ◽  
High Order ◽  
Energy Space ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Semilinear Evolution Equations

AbstractIn even space dimensions, the initial value problems for some high-order focusing semilinear evolution equations with exponential nonlinearities are considered. Using the potential well method, global and nonglobal well-posedness in the energy space are obtained.

scholarly journals A Family of High Order One-Block Methods for the Solution of Stiff Initial Value Problems

2019 ◽  
pp. 1-14
Author(s):  
I. J. Ajie ◽  
K. Utalor ◽  
P. Onumanyi
Keyword(s):  
Numerical Methods ◽  
Initial Value Problems ◽  
High Order ◽  
Numerical Implementation ◽  
Initial Value ◽  
Stiff Initial Value Problems ◽  
The Family ◽  
Block Methods ◽  
Backward Differentiation Formulas ◽  
Differentiation Formulas

In this paper, we construct a family of high order self-starting one-block numerical methods for the solution of stiff initial value problems (IVP) in ordinary differential equations (ODE). The Reversed Adams Moulton (RAM) methods, Generalized Backward Differentiation Formulas (GBDF) and Backward Differentiation Formulas (BDF) are used in the constructions. The E-transformation is applied to the triples and a family of self-starting methods are obtained. The family is for . The numerical implementation of the methods on some stiff initial value problems are reported to show the effectiveness of the methods. The computational rate of convergence tends to the theoretical order as h tends to zero.

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