-
Previous Article
Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate
- DCDS Home
- This Issue
-
Next Article
On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions
On asymptotic expansion solvers for highly oscillatory semi-explicit DAEs
1. | School of Electronic Engineering, Dublin City University, Dublin 9 |
2. | School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China |
3. | Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA |
References:
[1] |
W. E, A. Abdulle, B. Engquist and E. Vanden-Eijnden, The heterogeneous multiscale method, Acta Numer., 21 (2012), 1-87.
doi: 10.1017/S0962492912000025. |
[2] |
M. Condon, A. Deaño, J. Gao and A. Iserles, Asymptotic numerical algorithm for second order differential equations with multiple frequencies, Calcolo, 21 (2013), 1-31. |
[3] |
M. Condon, A. Deaño and A. Iserles, On Asymptotic-Numerical Solvers for Differential Equations with Highly Oscillatory Forcing Terms, DAMTP Tech. Rep. 2009/NA05. |
[4] |
M. Condon, A. Deaño and A. Iserles, On systems of differential equations with extrinsic oscillation, Discr. Cont. Dynamical Sys., 28 (2010), 1345-1367.
doi: 10.3934/dcds.2010.28.1345. |
[5] |
M. Condon, A. Deaño, A. Iserles and K. Kropielnicka, Efficient computation of delay differential equations with highly oscillatory terms, ESAIM Math. Model. Numer. Anal., 46 (2012), 1407-1420.
doi: 10.1051/m2an/2012004. |
[6] |
A. Iserles and S. P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. Royal Soc. A., 461 (2005), 1383-1399.
doi: 10.1098/rspa.2004.1401. |
[7] |
D. E. Johnson, J. R. Johnson and J. L. Hilburn, Electric Circuit Analysis, $2^{nd}$ edition, Prentice-Hall, New Jersey, 1992. |
[8] |
L. Malesani and P. Tenti, Three-phase AC/DC PWM converter with sinusoidal AC currents and minimum filter requirements, IEEE Trans. Ind. Appl., IA-23 (1987), 71-77.
doi: 10.1109/TIA.1987.4504868. |
[9] |
R. Pulch, Finite difference methods for multi time scale differential algebraic equations, ZAMM-Z Angew Math., 83 (2003), 571-583.
doi: 10.1002/zamm.200310042. |
[10] |
R. Pulch, M.Günther and S. Knorr, Multirate partial differential algebraic equations for simulating radio frequency signals, Eur. J. Appl. Math., 18 (2007), 709-743.
doi: 10.1017/S0956792507007188. |
[11] |
A. H. Robbins and W. Miller, Circuit Analysis: Theory and Practice, $5^{nd}$ edition, Cengage Learning, Boston, 2012. |
[12] |
J. M. Sanz-Serna, Modulated Fourier expansions and heterogeneous multiscale methods, IMA J. Numer. Anal., 29 (2009), 595-605.
doi: 10.1093/imanum/drn031. |
[13] |
R. E. Scheid, The accurate numerical solution of highly oscillatory ordinary differential equations, Math. Comp., 41 (1983), 487-509.
doi: 10.1090/S0025-5718-1983-0717698-9. |
[14] |
M. Selva Soto M. and C. Tischendorf, Numerical analysis of DAEs from coupled circuit and semiconductor simulation, Appl. Numer. Math., 53 (2005), 471-488.
doi: 10.1016/j.apnum.2004.08.009. |
[15] |
C. Tischendorf, Coupled Systems of Differential Algebraic and Partial Differential Equations in Circuit and Device Simulation, Modeling and numerical analysis, Habilitationsschrift, Inst. für Math., Humboldt-Univ. zu Berlin, 2004. |
show all references
References:
[1] |
W. E, A. Abdulle, B. Engquist and E. Vanden-Eijnden, The heterogeneous multiscale method, Acta Numer., 21 (2012), 1-87.
doi: 10.1017/S0962492912000025. |
[2] |
M. Condon, A. Deaño, J. Gao and A. Iserles, Asymptotic numerical algorithm for second order differential equations with multiple frequencies, Calcolo, 21 (2013), 1-31. |
[3] |
M. Condon, A. Deaño and A. Iserles, On Asymptotic-Numerical Solvers for Differential Equations with Highly Oscillatory Forcing Terms, DAMTP Tech. Rep. 2009/NA05. |
[4] |
M. Condon, A. Deaño and A. Iserles, On systems of differential equations with extrinsic oscillation, Discr. Cont. Dynamical Sys., 28 (2010), 1345-1367.
doi: 10.3934/dcds.2010.28.1345. |
[5] |
M. Condon, A. Deaño, A. Iserles and K. Kropielnicka, Efficient computation of delay differential equations with highly oscillatory terms, ESAIM Math. Model. Numer. Anal., 46 (2012), 1407-1420.
doi: 10.1051/m2an/2012004. |
[6] |
A. Iserles and S. P. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. Royal Soc. A., 461 (2005), 1383-1399.
doi: 10.1098/rspa.2004.1401. |
[7] |
D. E. Johnson, J. R. Johnson and J. L. Hilburn, Electric Circuit Analysis, $2^{nd}$ edition, Prentice-Hall, New Jersey, 1992. |
[8] |
L. Malesani and P. Tenti, Three-phase AC/DC PWM converter with sinusoidal AC currents and minimum filter requirements, IEEE Trans. Ind. Appl., IA-23 (1987), 71-77.
doi: 10.1109/TIA.1987.4504868. |
[9] |
R. Pulch, Finite difference methods for multi time scale differential algebraic equations, ZAMM-Z Angew Math., 83 (2003), 571-583.
doi: 10.1002/zamm.200310042. |
[10] |
R. Pulch, M.Günther and S. Knorr, Multirate partial differential algebraic equations for simulating radio frequency signals, Eur. J. Appl. Math., 18 (2007), 709-743.
doi: 10.1017/S0956792507007188. |
[11] |
A. H. Robbins and W. Miller, Circuit Analysis: Theory and Practice, $5^{nd}$ edition, Cengage Learning, Boston, 2012. |
[12] |
J. M. Sanz-Serna, Modulated Fourier expansions and heterogeneous multiscale methods, IMA J. Numer. Anal., 29 (2009), 595-605.
doi: 10.1093/imanum/drn031. |
[13] |
R. E. Scheid, The accurate numerical solution of highly oscillatory ordinary differential equations, Math. Comp., 41 (1983), 487-509.
doi: 10.1090/S0025-5718-1983-0717698-9. |
[14] |
M. Selva Soto M. and C. Tischendorf, Numerical analysis of DAEs from coupled circuit and semiconductor simulation, Appl. Numer. Math., 53 (2005), 471-488.
doi: 10.1016/j.apnum.2004.08.009. |
[15] |
C. Tischendorf, Coupled Systems of Differential Algebraic and Partial Differential Equations in Circuit and Device Simulation, Modeling and numerical analysis, Habilitationsschrift, Inst. für Math., Humboldt-Univ. zu Berlin, 2004. |
[1] |
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats. Averaging of highly-oscillatory transport equations. Kinetic and Related Models, 2020, 13 (6) : 1107-1133. doi: 10.3934/krm.2020039 |
[2] |
Wenlei Li, Shaoyun Shi. Singular perturbed renormalization group theory and its application to highly oscillatory problems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1819-1833. doi: 10.3934/dcdsb.2018089 |
[3] |
Kamil Aida-Zade, Jamila Asadova. Numerical solution to optimal control problems of oscillatory processes. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021166 |
[4] |
Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293 |
[5] |
Philippe Chartier, Norbert J. Mauser, Florian Méhats, Yong Zhang. Solving highly-oscillatory NLS with SAM: Numerical efficiency and long-time behavior. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1327-1349. doi: 10.3934/dcdss.2016053 |
[6] |
Claude Le Bris, Frédéric Legoll. Integrators for highly oscillatory Hamiltonian systems: An homogenization approach. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 347-373. doi: 10.3934/dcdsb.2010.13.347 |
[7] |
Emmanuel Frénod, Sever A. Hirstoaga, Eric Sonnendrücker. An exponential integrator for a highly oscillatory vlasov equation. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 169-183. doi: 10.3934/dcdss.2015.8.169 |
[8] |
Hermann Brunner. On Volterra integral operators with highly oscillatory kernels. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 915-929. doi: 10.3934/dcds.2014.34.915 |
[9] |
R.S. Dahiya, A. Zafer. Oscillatory theorems of n-th order functional differential equations. Conference Publications, 2001, 2001 (Special) : 435-443. doi: 10.3934/proc.2001.2001.435 |
[10] |
John R. Graef, R. Savithri, E. Thandapani. Oscillatory properties of third order neutral delay differential equations. Conference Publications, 2003, 2003 (Special) : 342-350. doi: 10.3934/proc.2003.2003.342 |
[11] |
Yoonsang Lee, Bjorn Engquist. Variable step size multiscale methods for stiff and highly oscillatory dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1079-1097. doi: 10.3934/dcds.2014.34.1079 |
[12] |
Zuji Guo, Zhaoli Liu. Perturbed elliptic equations with oscillatory nonlinearities. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3567-3585. doi: 10.3934/dcds.2012.32.3567 |
[13] |
Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991 |
[14] |
Elena Cordero, Fabio Nicola, Luigi Rodino. Time-frequency analysis of fourier integral operators. Communications on Pure and Applied Analysis, 2010, 9 (1) : 1-21. doi: 10.3934/cpaa.2010.9.1 |
[15] |
Kyril Tintarev. Positive solutions of elliptic equations with a critical oscillatory nonlinearity. Conference Publications, 2007, 2007 (Special) : 974-981. doi: 10.3934/proc.2007.2007.974 |
[16] |
Yu-Ting Lin, John Malik, Hau-Tieng Wu. Wave-shape oscillatory model for nonstationary periodic time series analysis. Foundations of Data Science, 2021, 3 (2) : 99-131. doi: 10.3934/fods.2021009 |
[17] |
Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky, Viktor Tkachenko, Serhiy Yanchuk. Frequency locking of modulated waves. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 847-875. doi: 10.3934/dcds.2011.31.847 |
[18] |
José M. Arrieta, Manuel Villanueva-Pesqueira. Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary. Communications on Pure and Applied Analysis, 2020, 19 (4) : 1891-1914. doi: 10.3934/cpaa.2020083 |
[19] |
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515 |
[20] |
José M. Arrieta, Ariadne Nogueira, Marcone C. Pereira. Nonlinear elliptic equations with concentrating reaction terms at an oscillatory boundary. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4217-4246. doi: 10.3934/dcdsb.2019079 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]