Applied and Computational Mathematics (ACM)

Multirate Partial Differential Algebraic Equations

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and/or frequency change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. On the one hand, the simulation of enveloppe-modulated signals requires the solution of initial-boundary value problems of the MPDAEs. On the other hand, the simulation of quasiperiodic signals implies multiperiodic boundary conditions only for the MPDAEs. In case of quasiperiodic signals, a method of characteristics solves the multirate model efficiently, since the system of partial differential algebraic equations exhibits a hyperbolic structure.

Publications

1985

128.

Spirko, Vladim{í}r; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H\(_{3}\)\(^{+}\)
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985

DOI: 10.1016/0022-2852(85)90203-6

127.

Spirko, Vladim{í}r; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H\(_{3}\)\(^{+}\)
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985

DOI: 10.1016/0022-2852(85)90203-6

126.

Spirko, Vladimír; Jensen, Per; Bunker, Philip R.; Cejchan, A.
The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+
Journal of Molecular Spectroscopy, 112 (1) :183-202
1985

DOI: 10.1016/0022-2852(85)90203-6

125.

Lamour, R.; Hanke, M.; Winkler, R.
The program system ‘RWA’ (version 2) for the solution of TPBVP - fundamentals and algorithms
, Seminarbericht 67 der Sektion MathematikBand67
Humboldt-Universität zu Berlin
1985
1984

124.

Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the \(\nu\)\(_{2}\) and \(\nu\)\(_{5}\) absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p84-039

123.

Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the \(\nu\)\(_{2}\) and \(\nu\)\(_{5}\) absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p84-039

122.

Morillon-Chapey, M.; Guelachvili, Guy; Jensen, Per
Analysis of the high resolution spectrum of the ν2 and ν5 absorption bands of methyl chloride
Canadian Journal of Physics, 62 (3) :247-253
1984
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p84-039

121.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984

DOI: 10.1016/0009-2614(84)80444-3

120.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984

DOI: 10.1016/0009-2614(84)80444-3

119.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984

DOI: 10.1016/0009-2614(84)80084-6

118.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules. b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984

DOI: 10.1016/0009-2614(84)80084-6

117.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984

DOI: 10.1016/0009-2614(84)80444-3

116.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984

DOI: 10.1016/0009-2614(84)80084-6

115.

Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984

DOI: 10.1016/0022-2852(84)90245-5

114.

Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984

DOI: 10.1016/0022-2852(84)90245-5

113.

Jensen, Per
C3O2 as a semirigid bender: The degenerate ν5 state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984

DOI: 10.1016/0022-2852(84)90245-5

112.

Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984

DOI: 10.1016/0022-2852(84)90058-4

111.

Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984

DOI: 10.1016/0022-2852(84)90058-4

110.

Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH3NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984

DOI: 10.1016/0022-2852(84)90058-4

109.

Glöckner, W.; Tausch, Michael W.; Autorenteam
MATERIALIEN FÜR DER KURSUNTERRICHT CHEMIE, Aufgabensammlung mit Klausur- und Abituraufgaben aus allen Bereichen der Schulchemie, 3 Bände
Herausgeber: Aulis Deubner\&Co KG, Köln
1984

108.

Winkler, R.
Numerische Behandlung von parameterabhängigen Zwei-Punkt-Randwertaufgaben unter Berücksichtigung von Verzweigungsproblemen
Humboldt-Universität zu Berlin
1984

107.

Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984

DOI: 10.1016/0047-2670(84)87043-4

106.

Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984

DOI: 10.1016/0047-2670(84)87043-4

105.

Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, Jürgen; Winter, R.; Zabel, Friedhelm
O2(a1Δg)-sensitized chemiluminescence of a1Δ → X3Σ- and b1Σ+ → X3Σ- transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984

DOI: 10.1016/0047-2670(84)87043-4

104.

Maten, E. J. W.
Stability analysis of finite difference methods for fourth order parabolic partial differential equations
Rijksuniversiteit Utrecht
1984