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The Numerical Solution of Laplace's Equation
Journal of Applied Physics, 1938This paper considers in detail numerical methods of solving Laplace's equation in an arbitrary two-dimensional region with given boundary values. The methods involve the solution of approximating difference equations by iterative procedures. Modifications of the standard Liebmann procedure are developed which lead to a great increase in the convenience
Shortley, G. H., Weller, R.
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On the Numerical Solution of the Hydrodynamic Equations
SIAM Review, 1961IN GENERAL, SOLUTIONS TO THE ONE-DIMENSIONAL, unisteady hydrodynamic equations can only be obtained by numerical integration. Several methods of performing such an integration are possible [1-6]. Thus a choice of method must be made, and unless this decision is made with care, considerable labor can be expended in arriving at the optimum method for the
Fyfe, I. M., Eng, R. C., Young, D. M.
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On the numerical solution of stiff systems
Applied Mathematics and Computation, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nuran Guzel, Mustafa Bayram
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Numerical Solutions by the Continuation Method
SIAM Review, 1973Summary: The continuation method is developed with a special emphasis on its suitability for numerical solutions on fast computers. Four problems are treated in detail: finding roots of a polynomial, boundary value problems of nonlinear equations, identification of parameters and eigenvalue problems of linear ordinary differential operators.
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The Numerical Solution of a Bifurcation Problem
SIAM Journal on Numerical Analysis, 1977For a completely continuous nonlinear equation $\lambda x = \mathcal{K}(x)$ with $\mathcal{K}(0) = 0$, approximate equations $\lambda x_n = \mathcal{K}_n (x_n )$, with $\mathcal{K}_n (0) = 0$, are analyzed. The family $\{ {\mathcal{K}_n } \}$ is collectively compact and pointwise convergent to $\mathcal{K}$. The existence and convergence of bifurcating
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Numerical Solution of Markov Chains
Numerical Linear Algebra with Applications, 2011SUMMARYThis special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16–17, 2010. The papers cover a broad range of topics including perturbation theory for absorbing chains, bounding techniques, steady‐state and transient solution methods,
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A NUMERICAL SOLUTION OF THE PROBLEM OF MOMENTS
Biometrika, 1947Hartley, H. O., Khamis, D. H.
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On a Numerical Solution of the Laplace Equation [PDF]
, 2015 The Laplace Equation in three variable can be reduced to three ODEs by means of the Fourier method. For the cases when the exact solution does not exist, or it is complicated,we apply the wavelet-Galerkin method to the ODEs. We use suitable wavelets or scaling functions that allow finding the numerical solutions of the three equations, which will form ...
Veta Buralieva, Jasmina +2 more
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Traveling wave solutions and numerical solutions of Gilson–Pickering equation
Results in Physics, 2021Khalid K Ali, M S Mehanna
exaly