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Original Articles

A Note on the Difference Schemes of the Nonlocal Boundary Value Problems for Hyperbolic Equations

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Pages 439-462 | Published online: 31 Aug 2006

References

  • Antonevich , A. , Belousov , M. and Lebedov , A. 1998 . Equations: II. C*-Applications. Part 2 Equations with Discontinuous Coefficients and Boundary Value Problems England : Addision Wesley Longman Limited .
  • Ashyralyev , A. 2003 . On well-posedness of the nonlocal boundary value problem for elliptic equations . Numer. Funct. Anal. Optimization , 24 ( 1–2 ) : 1 – 15 .
  • Ashyralyev , A. and Muradov , I. 1995 . “ On one difference scheme of second order of accuracy for hyperbolic equations. Proceeding of the IMM of AS of Turkmenistan ” . Vol. 3 , 58 – 63 . Russian : Ashgabat .
  • Ashyralyev , A. and Muradov , I. 1996 . On stability of difference scheme of a first order of accuracy for hyperbolic–parabolic equations . Izv. Akad. Nauk Turkmenistan Ser. Fiz.-Tekhn. Khim. Geol. Nauk , 2 : 35 – 39 . (Russian)
  • Ashyralyev , A. and Muradov , I. 1998 . “ On difference schemes second order of accuracy for hyperbolic–parabolic equations ” . In Modeling Processes in Exploitation of Gas Places and Applied Problems of Theoretical Gasohydrodynamics 127 – 138 . Ilim, , Russian : Ashgabat .
  • Ashyralyev , A. and Soltanov , H. 1998 . “ On one difference scheme for abstract nonlocal problem generating by the motion of gas in the homogenous space ” . In Modeling Processes in Exploitation of Gas Places and Applied Problems of Theoretical Gasohydrodynamics 147 – 154 . Ilim, Russian : Ashgabat .
  • Ashyralyev , A. and Sobolevskii , P. E. 2001 . A note on the difference schemes for hyperbolic equations . Abstr. Appl. Anal. , 16 ( 2 ) : 63 – 70 .
  • Ashyralyev , A. and Yurtsever , A. 2001 . On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations . Nonlinear Anal. Theory. Methods Appl. , 47 : 3585 – 3592 .
  • Ashyralyev , A. and Karatay , I. 2003 . On the second order of accuracy difference schemes of the nonlocal boundary value problem for parabolic equations . Funct. Differential Equations , 10 ( 1–2 ) : 45 – 63 .
  • Ashyralyev , A. and Sobolevskii , P. E. 2004 . New Difference Schemes for Partial Differential Equations BaselBoston, , Berlin : Birkhauser Verlag .
  • Ashyralyev , A. , Hanalyev , A. and Sobolevskii , P. E. 2001 . Coercive solvability of nonlocal boundary value problem for parabolic equations . Abstr. Appl. Anal. , 6 ( 1 ) : 53 – 61 .
  • Ashyralyev , A. , Karatay , I. and Sobolevskii , P. E. 2004 . On well-posedness of the nonlocal boundary value problem for parabolic difference equations . Discrete Dyn. Nat. Soc. , 2 : 273 – 286 .
  • Bazarov , D. and Soltanov , H. 1995 . Some Local and Nonlocal Boundary Value Problems for Equations of Mixed and Mixed-Composite Types Ilym, , Russian : Ashgabat .
  • Djuraev , T. D. 1979 . Boundary Value Problems for Equations of Mixed and Mixed-Composite Types Tashkent, , Russian : FAN .
  • Fattorini , H. O. 1985 . Second Order Linear Differential Equations in Banach Space North-Holland : Notas de Matematica .
  • Guidetti , D. , Karasozen , B. and Piskarev , S. 2001 . Approximation of abstract differential equations . Journal of Math. Sci. , 122 ( 2 ) : 3013 – 3054 .
  • Krein , S. G. 1966 . Linear Differential Equations in a Banach Space Moskow, , Russian : Nauka .
  • Mohamed , D. 1999 . Nonlocal boundary value problem for second order abstract elliptic differential equation . Abstr. Appl. Anal. , 4 ( 3 ) : 153 – 168 .
  • Salahatdinov , M. S. 1974 . Equations of Mixed-Composite Types Tashkent, , Russian : FAN .
  • Sobolevskii , P. E. and Chebotaryeva , L. M. Approximate solution by the method of lines of the Cauchy problem for abstract hyperbolic equations . Izv. Vyssh. Uchebn. Zav. Matematika , 5 103 – 116 . Russian

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