C. W. Cryer
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.
- 1 AHAMED, S. V., AND EDELYI, E. A. Nonlinear theory of salient pole machines. Trans. IEEE PAS-85 (1966), 61-70.Google Scholar
- 2 AMES, W. F. Nonlinear Partial Differential Equations in Engineering. Academic Press, New York, 1965.Google Scholar
- 3 CONCHS, P. Numerical solution of the nonlinear magnetostatic-field equation in two diruensions. J. Computational Phys. I (1966-67) (in press).Google Scholar
- 4 GREENSPAN, D. On approximating extremals of functionals. ICCC Bull. 4 (1965), 99-120.Google Scholar
- 5 ----. Introductory Numerical Analysis of Elliptic Boundary Value Problems. Harper and Row, New York, 1965.Google Scholar
- 6 KOSOLEV, A.I. Convergence of the method of successive approximations for quasi-linear elliptic equations. Soviet Math. 3 (1962), 219-222.Google Scholar
- 7 PEARSON, J. R.A. Non-Newtonian flow and die design. Trans. Plast. Inst. 30 (1962), 230- 239.Google Scholar
- 8 ----. Mechanical Principles of Polymer Melt Processing. Pergamon Press, London, 1965.Google Scholar
- 9 SCHECgTER, S. Iteration methods for non-linear problems. Trans. Amer. Math. Soc. 104 (1962), 179-189.Google Scholar
- 10 WINSLOW, A.M. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J. Computational Phys. 1 (1966-67), 149.Google Scholar
- 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.Google Scholar
Index Terms
- On the Numerical Solution of a Quasi-Linear Elliptic Equation
Recommendations
Fractional oscillator equation - Transformation into integral equation and numerical solution
In this paper we propose a numerical solution of a fractional oscillator equation (being a class of the fractional Euler-Lagrange equation). At first, we convert the fractional differential equation of order α 0 to an equivalent integral equation (...
Numerical approximations and solution techniques for the space-time Riesz---Caputo fractional advection-diffusion equation
In this paper, we consider a space-time Riesz---Caputo fractional advection-diffusion equation. The equation is obtained from the standard advection-diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of ...
Numerical solution of a parabolic equation with non-local boundary specifications
The parabolic partial differential equations with non-local boundary specifications model various physical problems. Numerical schemes are developed for obtaining approximate solutions to the initial boundary-value problem for one-dimensional second-...
Comments