Abstract
Many Important problems in engineering and physics require the solution of partial differential equations, such as Laplace's and Poisson's equqtions. In this paper, the method to solve the boundary problems of these equations with high accuracy and high calculation speed is discussed.
To solve the above equations, digital computers and registance networks are generally used. In this paper, the use of the Sampled Signal Analogue Computer which uses discrete analogue signals and lies between the digital computer and the registance networks is also proposed.
The errors of the solution consist of the discretization error ES, the operation error EC, and convergence error EN. These three errors are evaluated, and according to the result, the three apparatus are compared and discussed.
The digital computer is suitable to obtain solution of high accuracy (less than 0.1% in error) for the two dimentional problem.
The registance network is suitable to three dimentional problem and the solution of 0.01% in error can be obtained with the registance network of 0.1∼0.5% in accuracy.
The Sampled Signal Analogue Computer has accuracy of 0.5∼1% error, but the calculation time can be made shorter than the digital computer.
