Numerical Solution of Parabolic Partial Differential Equations With Two-Point Boundary Conditions by Use of the Method of Lines

ABSTRACT

The Method of Lines, a numerical technique commonly used for solving partial differential equations on analog computers, is used to attain digital computer solutions of such equations. An extensive theoretical development is presented that establishes convergence and stability for one-dimensional parabolic equations with Dirichlet boundary conditions. A new modification of the method, using noncentral differences, is shown to be much faster, in terms of computer time, than conventional grid methods, for two examples.

REFERENCES

• 1: FORSYTHE, G. E., aND WASOW, W. R. Finite Difference Methods for Partial DiflrenSsi Equations. Wiley, New York, 1960, p. 178.
• 2: Michael E. Fisher, Higher Order Differences in the Analogue Solution of Partial Differential Equations, Journal of the ACM (JACM), v.3 n.4, p.325-347, Oct. 1956 [doi>10.1145/320843.320852]
• 3: NORDSIECK, A. On numerieal integration of ordinary differential equations. Math. Collop. 16, 77 (Jan. 1962), 22-49.
• 4: COLLAR, A.R. On centrosymmetric and centroskew mtrices. Quart. J. Mech. and Appl Math. X, Pt. 3 (1962), 265-281.
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Experimentation, Measurement, Performance, Theory, Verification