On the Numerical Solution of a Quasi-Linear Elliptic Equation

ABSTRACT

A boundary value problem for the quasi-linear elliptic equation (xx/q2s)x + (xy/q2s)y = 0, where q2 = xx2 + xy2, 0 ≤ s < 1/2, is solved numerically, and the numerical process is analyzed mathematically.

REFERENCES

• 1: AHAMED, S. V., AND EDELYI, E. A. Nonlinear theory of salient pole machines. Trans. IEEE PAS-85 (1966), 61-70.
• 2: AMES, W. F. Nonlinear Partial Differential Equations in Engineering. Academic Press, New York, 1965.
• 3: CONCHS, P. Numerical solution of the nonlinear magnetostatic-field equation in two diruensions. J. Computational Phys. I (1966-67) (in press).
• 4: GREENSPAN, D. On approximating extremals of functionals. ICCC Bull. 4 (1965), 99-120.
• 5: ----. Introductory Numerical Analysis of Elliptic Boundary Value Problems. Harper and Row, New York, 1965.
• 6: KOSOLEV, A.I. Convergence of the method of successive approximations for quasi-linear elliptic equations. Soviet Math. 3 (1962), 219-222.
• 7: PEARSON, J. R.A. Non-Newtonian flow and die design. Trans. Plast. Inst. 30 (1962), 230- 239.
• 8: ----. Mechanical Principles of Polymer Melt Processing. Pergamon Press, London, 1965.
• 9: SCHECgTER, S. Iteration methods for non-linear problems. Trans. Amer. Math. Soc. 104 (1962), 179-189.
• 10: WINSLOW, A.M. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J. Computational Phys. 1 (1966-67), 149.
• 11: YOUNG, D. M., AND WHEELER, M.F. Alternating direction methods for solving partial difference equations, tn Nonlinear Problems of Engineering, Ames, W. F. (Ed.), Academic Press, New York, 1964.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Elliptic equations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Systems of equations

General Terms:
Measurement, Performance, Theory, Verification