Error bounds on some approximate solutions of the Fredholm equations and applications to potential scattering and bound state problems

1977 ◽  
Vol 18 (7) ◽  
pp. 1470-1475 ◽  
Author(s):  
S. R. Singh ◽  
G. Turchetti
Keyword(s):  
Error Bounds ◽  
Approximate Solutions ◽  
Bound State ◽  
Potential Scattering ◽  
Fredholm Equations

Linear regularizing algorithms for positive solutions of linear inverse problems

1988 ◽  
Vol 415 (1849) ◽  
pp. 257-275 ◽  
Keyword(s):  
Regularization Parameter ◽  
Numerical Differentiation ◽  
Approximate Solutions ◽  
Cauchy Problems ◽  
Negative Part ◽  
Fredholm Equations ◽  
Linear Inverse Problems ◽  
Ill Posed ◽  
Laplace Transform Inversion ◽  
Convolution Equations

Linear-regularization methods provide a simple technique for deter­mining stable approximate solutions of linear ill-posed problems such as Fredholm equations of the first kind, Cauchy problems for elliptic equations and backward solution of forward parabolic equations. In most of these problems the solution must be positive to satisfy physical plausibility. In this paper we consider ill-posed first-kind convolution equations and related problems such as numerical differentiation, Radon transform and Laplace-transform inversion. We investigate several linear regularization algorithms which provide positive approximate solutions for these problems at least in the absence of errors on the data. For noisy data the solution is not necessarily positive. Because the appearance of negative values can then only be an effect of the noise, the negative part of the solution should be negligible with a suitable choice of the regularization parameter. A price to pay for ensuring positivity is always, however, a reduction in resolution.

scholarly journals Magneto-micropolar fluid motion: global existence of strong solutions

1999 ◽  
Vol 4 (2) ◽  
pp. 109-125 ◽  
Author(s):  
Elva E. Ortega-Torres ◽  
Marko A. Rojas-Medar
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Error Bounds ◽  
Micropolar Fluid ◽  
Fluid Motion ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Time Estimates ◽  
Spectral Galerkin Method ◽  
External Forces

By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of magneto-micropolar fluid without assuming that the external forces decay with time. We also derive uniform in time estimates of the solution that are useful for obtaining error bounds for the approximate solutions.

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