scholarly journals An algorithm based on DQM with modified trigonometric cubic B-splines for solving coupled viscous Burgers' equations

2018 ◽  
Vol 2018 (1) ◽  
pp. 21-41
Author(s):  
Brajesh Kumar Singh ◽  
Pramod Kumar
Keyword(s):  
B Splines ◽  
Burgers Equations

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

2021 ◽  
Vol 381 ◽  
pp. 113779
Author(s):  
Wenbin Hou ◽  
Kai Jiang ◽  
Xuefeng Zhu ◽  
Yuanxing Shen ◽  
Ping Hu
Keyword(s):  
Isogeometric Analysis ◽  
B Splines ◽  
Discontinuous Problems

scholarly journals Interpolation and Sampling with Exponential Splines of Real Order

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Massopust
Keyword(s):  
Positive Real ◽  
B Splines

AbstractThe existence of fundamental cardinal exponential B-splines of positive real order $$\sigma $$ σ is established subject to two conditions on $$\sigma $$ σ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented.

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

Non-uniform subdivision for B-splines of arbitrary degree

2009 ◽  
Vol 26 (1) ◽  
pp. 75-81 ◽  
Author(s):  
S. Schaefer ◽  
R. Goldman
Keyword(s):  
Arbitrary Degree ◽  
B Splines
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