Computational strategies for the tension parameters of the exponential spline

2006 ◽  
pp. 122-134 ◽  
Author(s):  
P. Rentrop ◽  
U. Wever
Keyword(s):  
Exponential Spline

scholarly journals Orthogonal Exponential Spline Pulses with Application to Impulse Radio

2011 ◽  
Vol 10 (1-2) ◽  
pp. 1-16
Author(s):  
Masaru Kamada ◽  
Semih Özlem ◽  
Hiromasa Habuchi
Keyword(s):  
Impulse Radio ◽  
Exponential Spline

scholarly journals Partially penetrating slug tests in an unweathered till layer

2016 ◽  
Vol 48 (1) ◽  
pp. 117-132
Author(s):  
David W. Ostendorf ◽  
William G. Lukas ◽  
Don J. DeGroot
Keyword(s):  
Laplace Transform ◽  
Spline Function ◽  
Inverse Laplace Transform ◽  
Short Term ◽  
Slug Test ◽  
Slug Tests ◽  
Monitoring Wells ◽  
Exponential Spline ◽  
Eastern Massachusetts

This research improves field based estimates of aquitard compressibility and permeability. A semianalytical model of partially penetrating, overdamped slug tests achieves this objective. The short term solution is an existing fully penetrating model, the long term solution is the polar residue of an inverse Laplace transform, and an exponential spline function patches the solutions together. Large amplitude slug test data from ten pairs of partially penetrating monitoring wells installed in an unweathered till at Scituate Hill in eastern Massachusetts calibrate the model. The deposit is bound by weathered till and the Dedham Granite fracture zone, and both are far more permeable than the unweathered till. The calibrated till permeability of 8.4 × 10–16 m2 is about 25% less than existing model calibrations that include boundary recharge in permeability values. The calibrated till compressibility of 5.1 × 10–10 Pa–1 reflects the proper inclusion of recharge as a long term source of groundwater, rather than the unrealistically large compressibility calibrations required by fully penetrating models.

An exponential spline interpolation for unequally spaced data points

1982 ◽  
Vol 28 (1) ◽  
pp. 61-67 ◽  
Author(s):  
V. Tornow
Keyword(s):  
Spline Interpolation ◽  
Unequally Spaced ◽  
Exponential Spline ◽  
Data Points

scholarly journals The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers

2015 ◽  
Vol 3 ◽  
pp. 186
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Problem ◽  
Elliptic Type ◽  
Exponential Spline ◽  
Initial Boundary Value

<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p>The special parabolic and exponential spline, which interpolation middle integral values of piece-wise smooth function, are considered. With the help of this splines is reduce the problems of mathematical physics in 3-D with piece-wise coefficients to respect one coordinate to problems for system of equations in 2-D. This procedure allows reduce the 3-D problem to a problem of 2-D and 1-D problems and the solution of the approximated problem is obtained analytically.</p><p>The solution of corresponding averaged 2-D initial-boundary value problem is obtained also numerically, using for approach differential equations the discretization in space applying the central differences. The approximation of the 2-D non-stationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.</p>

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