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Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Luis Cueto-Felgueroso, Ruben Juanes
2009 Journal of Computational Physics  
This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems.  ...  The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers.  ...  Acknowledgements We gratefully acknowledge funding for this research, provided by Eni under the Multiscale Reservoir Science project, and by the ARCO Career Development Chair.  ... 
doi:10.1016/j.jcp.2009.05.045 fatcat:sh53ccxfazge7bo2fbtwhbqhgy

Page 5664 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
The contribution shows recent progress in fourth-order spatial differencing methods.  ...  In contrast to the second-order spectral viscosity (SV) method, in the SSV method a Chebyshev differential operator of high order is applied.  ... 

List of contents

2002 Computers and Mathematics with Applications  
of Relaxation Schemes for Initial Boundary Value Problems for Conservation Laws Symplectic and Multi-Symplectic Methods for the Nonlinear Schrodinger Equation Lower Bounds in Spectral Tests  ...  , Radial Basis Functions, and Toeplitz Matrices Grid-Free Adaptive Semi-Lagrangian Advection Using Radial Basis Functions Stability Analysis of Particle Methods with Corrected Derivatives Numerical  ... 
doi:10.1016/s0898-1221(02)80024-4 fatcat:5k7lu3scvfb2hkwneva6q73x24

Page 1565 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Summary: “An oscillation method is presented for finding the eigenvalues of a fourth-order, selfadjoint, two-point boundary value problem.  ...  {For the entire collection see MR 91m:65005.} 92c:65094 65L15 34B99 Greenberg, Leon (1-MD) An oscillation method for fourth-order, selfadjoint, two-point boundary value problems with nonlinear eigenvalues  ... 

author index volume

2007 Journal of Computational and Applied Mathematics  
Tasci, Factorizations and representations of the backward second-order linear recurrences 182-197 Kohr, M., Boundary value problems for a compressible Stokes system in bounded domains in R n 128-145 Kreiss  ...  Meek, Planar interpolation with a pair of rational spirals 112-127 Graves-Morris, P.R., BiCGStab, VPAStab and an adaptation to mildly nonlinear systems 284-299 Hara, T., see Yoshida, N. 339-347 Heinkenschloss  ... 
doi:10.1016/s0377-0427(07)00020-9 fatcat:j4fmvomqsrgexhd32bznrsb4du

Author index to volumes 71–80

1997 Journal of Computational and Applied Mathematics  
Valent, Fourth-order difference equation for the associated Meixner and Charlier polynomials Levin, D., Analysis of a collocation method for integrating rapidly oscillatory functions Lewanowicz, S., Recurrence  ...  Simos, A generator of high-order embedded P-stable methods for th e nume rical solution of the Schrodinger equa tion Axelsson, 0., The stabilized V-cycle method Axelsson, O. and H.  ... 
doi:10.1016/s0377-0427(97)80100-8 fatcat:aweisaflbbg4hbkwa2c6efh4c4

Page 1479 of Mathematical Reviews Vol. , Issue 81D [page]

1981 Mathematical Reviews  
Author’s summary: “Systematic methods are presented for obtain- ing recurrence relations for the coefficients in CebySev series solu- tions of linear differential equations of first to fourth order with  ...  René Alt (Paris) 81d:65041 Gekeler, Eckart 81d:65042 Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems. Internat. J. Math. Math.  ... 

Master index to volumes 1–10

1984 Journal of Computational and Applied Mathematics  
7 (2) Papamiehael, N. and Worsey, A.J., A cubic spline method for the solution of a linear fourth-order two-point boundary value problem 7 (3) Papatheodorou, T.S., Inverses for a class of banded matrices  ...  finite difference method for computing eigenvalues of fourth-order two-point boundary value problems (Short Communication) Chawla, M.M. and Sharma, S.R., Absolute stability of explicit Runge-Kutta-NystriSm  ... 
doi:10.1016/0377-0427(84)90048-7 fatcat:u3omdjyvtfc35ev2ohkk32exsu

Second Symposium on "Recent Trends in the Numerical Solution of Differential Equations": Preface

Luigi Brugnano, Theodore E. Simos, George Psihoyios, Ch. Tsitouras
2009 AIP Conference Proceedings  
Phys. 53, 102702 (2012) Existence and stability of standing waves for nonlinear fractional Schrödinger equations J. Math.  ...  Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations J. Math.  ...  In order to obtain an approximation of the potential, a sequence of direct problems is solved by methods in the family of BVMs.  ... 
doi:10.1063/1.3241563 fatcat:a5kushymqfexpni6dcprpmd22u

Page 5582 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Van Loan, The block Jacobi method for computing the singular value decomposition (pp. 245-255); Dao Yi Xu, Stability criteria for interval matrices (pp. 257-261).  ...  Penev, Adaptive tracking of the programmed motion of nonlinear nonstationary systems (pp. 129-138, 182); V. K.  ... 

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

Hector Gomez, Luis Cueto-Felgueroso, Ruben Juanes
2013 Journal of Computational Physics  
The extended model is based on a phase-field formulation and is fourth-order in space.  ...  We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient  ...  These methods are widely used for fourth-order partial differential equations in which the fourth-order term is linear.  ... 
doi:10.1016/j.jcp.2012.12.018 fatcat:5jva5bxvonfr3pypqxhvf22tra

Page 1232 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Trummer, Spectral methods in computing invariant tori (275-292); Guido Van den Heuvel, New stability results for Runge-Kutta methods adapted to delay differential equations (293-308); Barbara Zubik-Kowal  ...  Nakao and Yoshitaka Watanabe, Validated computation for a linear elliptic problem with a parameter (155-162); De-Hao Yu, The natural integral operators and the domain decomposition methods for 3-D exterior  ... 

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Milošević, On the new fourth-order methods for the simultaneous approximation of polynomial zeros 4059-4075 Phuengrattana, W. and S.  ...  Zhang, A fourth-order derivative-free algorithm for nonlinear equations 2551-2559 Peng, H.-J., Z.-G. Wu and W.-X.  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

Author Index Volumes 131–140

2002 Journal of Computational and Applied Mathematics  
Schein, Adaptive schemes for the numerical solution of SDEs*a comparison 138 (2002) 297}308 Letessier, J., Fourth-order di!  ...  Kumar, A fourth-order "nite-di!erence method based on non-uniform mesh for a class of singular two-point boundary Bai, Z.-Z. and C.-L.  ... 
doi:10.1016/s0377-0427(02)00366-7 fatcat:gjrcl5wajbe3hom4ssqq3jfjkq

Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability

Viet-Thanh Pham, Sundarapandian Vaidyanathan, Tomasz Kapitaniak
2020 Complexity  
Multistability is a critical property of nonlinear dynamical systems, where a variety of phenomena such as coexisting attractors can appear for the same parameters but with different initial conditions  ...  Circuit design (numerical and hardware) of multistable systems is a related research problem with real-world applications, and fractional-order modelling and realization of multistable systems also constitute  ...  For this instability problem, Z.  ... 
doi:10.1155/2020/8510930 fatcat:hhq5u6efebcvjjwozeegx7dolm
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