Stable difference schemes with uneven mesh spacings

Author:
Melvyn Ciment

Journal:
Math. Comp. **25** (1971), 219-227

MSC:
Primary 65N10

MathSciNet review:
0300470

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Abstract: We consider a finite-difference approximation to the Cauchy problem for a firstorder hyperbolic partial differential equation using different mesh spacings in different portions of the domain. By reformulating our problem as a difference approximation to an initial-boundary value problem, we are able to use the theory of H. O. Kreiss and S. Osher to analyze the stability of our scheme.

**[1]**M. Ciment,*Stable Difference Schemes With Uneven Mesh Spacings*, A.E.C. Research and Development Report #NYO-1480-100, Ph.D. Thesis, New York University, New York, 1968.**[2]**Eugene Isaacson and Herbert Bishop Keller,*Analysis of numerical methods*, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR**0201039****[3]**Heinz-Otto Kreiss,*Difference approximations for the initial-boundary value problem for hyperbolic differential equations*, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966) John Wiley & Sons, Inc., New York, 1966, pp. 141–166. MR**0214305****[4]**Heinz-Otto Kreiss,*Stability theory for difference approximations of mixed initial boundary value problems. I*, Math. Comp.**22**(1968), 703–714. MR**0241010**, 10.1090/S0025-5718-1968-0241010-7**[5]**Peter D. Lax and Burton Wendroff,*Difference schemes for hyperbolic equations with high order of accuracy*, Comm. Pure Appl. Math.**17**(1964), 381–398. MR**0170484****[6]**Stanley Osher,*Systems of difference equations with general homogeneous boundary conditions*, Trans. Amer. Math. Soc.**137**(1969), 177–201. MR**0237982**, 10.1090/S0002-9947-1969-0237982-4**[7]**Robert D. Richtmyer and K. W. Morton,*Difference methods for initial-value problems*, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0220455**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1971-0300470-3

Keywords:
Difference methods,
stability,
mixed initial-boundary value problems,
mesh refinement

Article copyright:
© Copyright 1971
American Mathematical Society