A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

2006 ◽  
Vol 2 (1/2) ◽  
pp. 45 ◽  
Author(s):  
M.S. Sahimi ◽  
N.A. Mansor ◽  
N.M. Nor ◽  
N.M. Nusi ◽  
N. Alias
Keyword(s):  
Heat Equation ◽  
High Accuracy ◽  
Explicit Method

scholarly journals A Meshless Method to Determine a Source Term in Heat Equation with Radial Basis Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Baiyu Wang ◽  
Anping Liao
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Radial Basis Functions ◽  
Meshless Method ◽  
Source Term ◽  
Initial Boundary ◽  
High Accuracy ◽  
Basis Functions ◽  
Unknown Source ◽  
Radial Basis

This paper considers a numerical method based on the radial basis functions for the inverse problem of heat equation; the inverse problem is determining an unknown source term subject to the overdetermination along with the usual initial boundary conditions, and the unknown source term is only time-dependent. The radial basis functions method is a meshless method with high accuracy for the inverse problem. Some numerical experiments using this method are presented and discussed.

scholarly journals The Numerical Solution of Heat Equation by the Fourth-Order Iterative Alternating Decomposition Explicit Method with MPI

2019 ◽  
Vol 8 (6S3) ◽  
pp. 4-9
Keyword(s):  
Heat Equation ◽  
Numerical Solution ◽  
Fourth Order ◽  
Message Passing ◽  
Message Passing Interface ◽  
Finite Difference Methods ◽  
Explicit Method ◽  
Time Step ◽  
Accelerate Convergence ◽  
Parallel Platform

The numerical solution of the heat equation in one space dimension is obtained using the Fourth-Order Iterative Alternating Decomposition Explicit Method (4-IADE) on a parallel platform with Message Passing Interface (MPI). Here, a higher fourth-order Crank-Nicolson type scheme is used in the approximation which gives rise to a Penta diagonal matrix in the solution of the system at each time level. The method employs a splitting strategy which is applied alternately at each half time step. The method is shown to be computationally stable and appropriate parameters chosen to accelerate convergence. The accuracy of the method is comparable to that of existing well known methods. Results obtained by this method for several different problems were compared with the exact solution and agreed closely with those obtained by other finite-difference methods with correlation between speedup and efficiency

Laplace inversion for the solution of an abstract heat equation without the forward transform of the source term

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Shu-Lin Wu
Keyword(s):  
Heat Equation ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Source Term ◽  
Finite Interval ◽  
Quadrature Rule ◽  
High Accuracy ◽  
Laplace Inversion ◽  
Finite Set ◽  
Complex Coefficients

AbstractWe consider the discretization in time of inhomogeneous parabolic equations, using the technique of Laplace inversion along a contour located in the complex left half-plane which, after transformation to a finite interval, is then evaluated to high accuracy by a contour quadrature rule. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. A serious problem is how to treat the source term

A New 1,000 kV Electron Microscope

1967 ◽  
Vol 25 ◽  
pp. 260-261
Author(s):  
M. Nishigaki ◽  
S. Katagiri ◽  
H. Kimura ◽  
B. Tadano
Keyword(s):  
Electron Microscope ◽  
High Voltage ◽  
Basic Research ◽  
Chromatic Aberration ◽  
High Accuracy ◽  
Biological Specimen ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
High Voltage Electron

The high voltage electron microscope has many advantageous features in comparison with the ordinary electron microscope. They are a higher penetrating efficiency of the electron, low chromatic aberration, high accuracy of the selected area diffraction and so on. Thus, the high voltage electron microscope becomes an indispensable instrument for the metallurgical, polymer and biological specimen studies. The application of the instrument involves today not only basic research but routine survey in the various fields. Particularly for the latter purpose, the performance, maintenance and reliability of the microscope should be same as those of commercial ones. The authors completed a 500 kV electron microscope in 1964 and a 1,000 kV one in 1966 taking these points into consideration. The construction of our 1,000 kV electron microscope is described below.

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