A high-accuracy algorithm for solving nonlinear PDEs with high-order spatial derivatives in 1 + 1 dimensions

Journal Article · Wed Jun 01 00:00:00 EDT 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1108· OSTI ID:7073524

Yao, Jian Hua; Gooding, R J ^[1]

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1. Queen's Univ., Kingston, Ontario (Canada)

We propose an algorithm to solve a system of partial differential equations of the type u[sub t](x,t) = F(x, t, u, u[sub x], u[sub xx], u[sub xxx], u[sub xxxx]) in 1 + 1 dimensions using the method of lines with piecewise ninth-order Hermite polynomials, where u and F and N-dimensional vectors. Nonlinear boundary conditions are easily incorporated with this method. We demonstrate the accuracy of this method through comparisons of numerically determine solutions to the analytical ones. Then, we apply this algorithm to a complicated physical system involving nonlinear and nonlocal strain forces coupled to a thermal field. 4 refs., 5 figs., 1 tab.

• OSTI ID: 7073524
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 112:2; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ACCURACY
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
WAVE EQUATIONS