Chaplygin's method is Newton's method
Copyright policy )Chaplygin's method is Newton's method
This method has been extended to ordinary differential equations in [w” by Lusin [6], to ordinary differential equations in Banach spaces by Mlak [8] and to parabolic equations by Mlak [7] and Szarki [15, Sect. 661. In each case a different type of hypotheses is assumed. A formal generalization considered by Wazewski [18] has been found by Schelkunoff [14] t o b e useful in the antenna problem, and has been compared to the classical successive approximations by Olech [9]. In the literature, Chaplygin’s method is apparently considered as an analog or a variant of Newton’s method, although no explicit comparison seems to exist. The aim of this note is to prove that they are the same thing in the sense that the Chaplygin sequence is exactly the Newton sequence for the operator
Volterra integral equations, Numerical solutions to equations with nonlinear operators, Applied Mathematics, Newton's Method, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Partial differential equations, Numerical methods for initial value problems involving ordinary differential equations, Boundary value problems, Ordinary Differential Equations, Initial Value Problems, Numerical Methods, Chaplygin's Method, Initial Value Problem, Integral equations, Analysis
Volterra integral equations, Numerical solutions to equations with nonlinear operators, Applied Mathematics, Newton's Method, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Partial differential equations, Numerical methods for initial value problems involving ordinary differential equations, Boundary value problems, Ordinary Differential Equations, Initial Value Problems, Numerical Methods, Chaplygin's Method, Initial Value Problem, Integral equations, Analysis
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!