المرجع الألكتروني للمعلوماتية
القرآن الكريم وعلومه
العقائد الإسلامية
الفقه وأصوله 
الرجال والحديث 
سيرة الرسول وآله 
علوم اللغة العربية 
الأدب العربي 
الأسرة والمجتمع 
الأخلاق والأدعية 
التاريخ 
الادارة والاقتصاد 
علم الفيزياء 
علم الكيمياء 
علم الأحياء 
الرياضيات 
الهندسة المدنية 
الزراعة 
الجغرافية 
القانون 
اللغة الأنكليزية 
الأخبار 
الإعلام 
مكتبة الصور 
أقلام بمختلف الألوان 
إضاءات
مفتاح
أجوبة الإستفتاءات الشرعية
وثائقيات
تاريخ الرياضيات
الرياضيات في الحضارات المختلفة
الرياضيات المتقطعة
الجبر
الهندسة
المعادلات التفاضلية و التكاملية
التحليل
علماء الرياضيات | John Crank |
 32
 02:27 مساءً
date: 1-1-2018 |
Author : J Crank 
Book or Source : Free and moving boundary problems 
Page and Part : ...|
Read More
Date: 8-1-2018
150
Date: 1-1-2018
44
Date: 1-1-2018
42
|
Died: 3 October 2006
John Crank was a student of Lawrence Bragg and Douglas Hartree at Manchester University (1934-38), where he was awarded the degrees of B.Sc. and M.Sc. and later (1953) D.Sc. After war work on ballistics he was a mathematical physicist at Courtaulds Fundamental Research Laboratory from 1945 to 1957 and professor of mathematics at Brunel University (initially Brunel College in Acton) from 1957 to 1981. His main work was on the numerical solution of partial differential equations and, in particular, the solution of heat-conduction problems. In the 1940s such calculations were carried out on simple mechanical desk machines. Crank is quoted as saying that to "burn a piece of wood" numerically then could take a week.
John Crank is best known for his joint work with Phyllis Nicolson on the heat equation, where a continuous solution u(x, t) is required which satisfies the second order partial differential equation
ut - uxx = 0
for t > 0, subject to an initial condition of the form u(x, 0) = f (x) for all real x. They considered numerical methods which find an approximate solution on a grid of values of x and t, replacing ut(x, t) and uxx(x, t) by finite difference approximations. One of the simplest such replacements was proposed by L F Richardson in 1910. Richardson's method yielded a numerical solution which was very easy to compute, but alas was numerically unstable and thus useless. The instability was not recognised until lengthy numerical computations were carried out by Crank, Nicolson and others. Crank and Nicolson's method, which is numerically stable, requires the solution of a very simple system of linear equations (a tridiagonal system) at each time level.
Books:
Articles:
|
|
|
|
مخاطر عدم علاج ارتفاع ضغط الدم
|
|
|
|
|
|
|
اختراق جديد في علاج سرطان البروستات العدواني
|
|
|
|
|
|
|
نشر مظاهر الفرح في مرقد أبي الفضل العباس بذكرى ولادة السيدة زينب (عليهما السلام)
|
|
|
