Non-spurious solutions to second order BVP by monotonicity methods

2016/06/22 by Filip Pietrusiak, Pietrusiak, Filip
Mathematics · #30E25 #34B15 #39A10 #39A12 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1606.07120

openalex publication_date 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following BVP x( t) =f( t,x( t) ,x( t) ) -h( t) , % x( 0) =x( 1) =0, where f is continuous and satisfies some other conditions, h∈ H₀¹( 0,1) together with its discretization -Δ²x(k-1)+\frac1n²f((k)/(n), nΔx(k-1), x(k))=\frac1n²h((k)/(n)), k∈ \1, 2, …,n \. Using monotonicity methods we obtain the convergence of a solutions to a family of discrete problems to the solution of a continuous one, i.e. the existence of non-spurious solutions to the above problems is considered. Continuous dependence on parameters for the continuous problem is also investigated.

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