Numerical Solution of Linear Integral Equations of the First Kind. Calculation of Molecular Weight Distributions from Sedimentation Equilibrium Data

1967 ◽  
Vol 46 (8) ◽  
pp. 3229-3236 ◽  
Author(s):  
S. W. Provencher
Keyword(s):  
Molecular Weight ◽  
Numerical Solution ◽  
Integral Equations ◽  
Sedimentation Equilibrium ◽  
Molecular Weight Distributions ◽  
Weight Distributions ◽  
Equilibrium Data ◽  
Linear Integral ◽  
Linear Integral Equations

A note on the numerical solution of certain non-linear integral equations

1956 ◽  
Vol 236 (1207) ◽  
pp. 529-534 ◽  
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Asymptotic Form ◽  
Essential Singularity ◽  
Non Linear ◽  
Linear Integral ◽  
Hydrodynamical Problem ◽  
Linear Integral Equations

Methods are described for the numerical solution of two non-linear integral equations occurring in a hydrodynamical problem. In each case the existence of an essential singularity of the solution requires the application of special techniques. The asymptotic form of the solutions for large x is determined.

The numerical solution of non-singular linear integral equations

1953 ◽  
Vol 245 (902) ◽  
pp. 501-534 ◽  
Keyword(s):  
Finite Difference ◽  
Eigenvalue Problem ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Numerical Quadrature ◽  
Iterative Processes ◽  
Upper Limit ◽  
Linear Integral ◽  
Linear Integral Equations

The integral equations discussed and illustrated are those of Fredholm, with fixed limits in the integral and including the eigenvalue problem, and of Volterra, with a variable upper limit in the integral. The methods are mostly based on finite-difference theory, the integrals being replaced by formulae for numerical quadrature. Computational details are given for several methods, and there is a discussion of error analysis for Volterra’s equation. Some methods are given for accelerating the convergence of classical iterative processes.

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