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Finite difference schemes for a generalized Calcium diffusion equation

이남용|추상목
영남수학회 (Youngnam Mathematical Society)|2008.09|East Asian Mathematical Journal|제24권 제4호|pp. 407-414

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참고문헌

키워드

bufferconvectionerror estimatesCa^{2+} diffusion equationnonlinear difference schemesLax-Richtmyer equivalence theorem
주제분류수학

초록

Finite difference schemes are considered for a Ca^{2+} diffusion equations with damping and convection terms, which describe Ca^{2+} buffering by using stationary and mobile buffers. Stability and L^{∞} error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

Abstract

Finite difference schemes are considered for a Ca^{2+} diffusion equations with damping and convection terms, which describe Ca^{2+} buffering by using stationary and mobile buffers. Stability and L^{∞} error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

참고문헌 (13)

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  2. V. E. Bondarenko, "Computer model of action potential of mouse ventricular myocytes", Am J Physiol Heart Circ Physiol, 287, pp.378~403 (2004)
  3. S. M. Choo, "conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation", J. Appl. Math. Comput, 16, pp.53~68 (2004)
  4. 추상목, "Error estimates of nonstandard finite difference schemes for generalized Cahn-Hilliard and Kuramoto-Sivashinsky equations", 대한수학회지, 42(6), pp.1121~1136 (2005), 대한수학회
  5. M. Falcke, "Buffers and oscillations in intracellular Ca2+ dynamics", Biophys J, 84, pp.28~41 (2003)
  6. J. L. Greenstein, "An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release", Biophys J, 83, pp.2918~2945 (2002)
  7. T. J. Hund, "Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model", Circulation, 110, pp.3168~3174 (2004)
  8. M. S. Jafri, "Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load", Biophys J, 74, pp.1149~1168 (1998)
  9. J. C. Lopez-Marcos, "Stability and convergence in numerical analysis III: Linear investigation of nonlinear stability", IMA J. Numer. Anal, 8, pp.71~84 (1988)
  10. A. Michailova, "Spatiotemporal features of Ca2+ buffering and diffusion in atrial cardiac myocytes with inhibited sarcoplasmic reticulum", Biophys J, 83, pp.3134~3151 (2002)
  11. R. E. Milner, "Calcium binding proteins in the sarcoplasmic", endoplasmic reticulum of muscle and nonmuscle cells, 1992, pp.112, 1~13
  12. D. E. Strier, "Saltatory and continuous calcium waves and the rapid buffering approximation", Biophys J, 85, pp.3575~3586 (2003)
  13. J. Wagner, "Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations", Biophys J, 67, pp.447~456 (1994)

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