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A Semi Analytical Investigation of the Paracial Ray Equation | ||
| Journal of College of Education | ||
| Article 1, Volume 0, Issue 3, 2017, Pages 117-132 | ||
| Author | ||
| Hassan N. Al-Obaidi | ||
| Abstract | ||
| A new common procedure for solving paraxial ray equation of a charge particle going thiough a pure magnetic field has been introduced. The-prlsented approach ii nrainly concem with using power series method usually ,."a to solve differential equations of special forms. In order to rnake the power series method applicable for solving equations of soft of paraxial ray equation, the domain of solution, the axial coordinate where the magnetic field exist, are descretized into several subdomains, such that -magnetic field can consider to be flxed throughout each of these subdomains. computer has been adopted to be u n,uin tool for execution i, order to make prqsent technique of a practical impoftance. The outputs of this procedure are conlpared rvith some of the available conespondence anall'tical equations' The results clearly shorvn that the neu'technigue have an accurate results and has the i.op..ry of analytical proce{ure. Anyrvay, the algorithnr of pr.r.nt.d method are formulated to a subroutine written in Fortrarr-77 iungrog" rvhich nray used to replace any of the subroutines that work ,n,ith ,rumerical ntethods in the well knorvn software. Hott'ever, one u'ould not face the nurlerical errors any more. | ||
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