It is important to choose the method of solution to calculate a magnetic field problem. Recently numerical methods are expanding widely in their applications instead of analytical methods.
In this paper some of the recent applications of numerical methods to the analysis of electrical engineering problems, particularly a finite element method and an integral equation method, are reviewed. In addition a comparison of featurs of above two methods and their problems for practical use are described.

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Computational aspects of the F. E. M Solutions of the convective transport equations:∂tu+∇·(-k∇u+bu)=for∇·(-k∇u+bu)=f are described. Substructured Iteration Methods and Preconditioned LU & Conjugate Gradient Methods are feasible to overcome the memory neck of the computers. ICCG by Meijerink and Van der Vorst are applied to the 3 dimensional ∇·(-k∇u)=f with variable diffusion coefficient k and compared to the SOR, SLOR, and Pure CG Methods.

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Magnetic field calculations by using the finite element method are summarized and its recent prospects are described.
The finite element method is used to design smaller electrical machinery and improve its efficiency. Many analyzed examples of power apparatus such as transformers and rotating machineries, and electronic instruments such as electronic watches, electromagnets, speakers, magnetic heads, electromagnetic cookers are shown. This method is also effective for the investigation of the flux and the eddy current distributions in conductors or silicon steels, and for the design of magnetic circuits under specified conditions.

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A brief review of the theory of magnetic recording is given with emphasis on analytical studies of head field, the recording process and the read-out process.
Treatments are made of perpendicular recording and the magnetoresistive head in addition to conventional magnetic recording.
There are many complications in magnetic recording, some of which are due to magnetic saturation, recording-demagnetization, and the magnetic interaction between the head and the medium. The analytical studies are not only useful in designing components such as the recording head and the recording medium, but also in the designing of systems.
Of primary importance for the analytical studies is the choice of a suitable model.
The numerical analysis method is indispensable to the studies, since, in many cases, it is difficult to solve the model analytically because of non-linearity and hysteresis of the head and the recording medium.
The purposes of this paper are to explain some important characteristics of magnetic recording, to discuss some models of the head and the recording and read-out processes, and to review some methods of numerical analysis.

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