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الحل العددي لبعض المعادلات التفاضليه باستخدام تحويل لاكير == Numerical Solution for some Differential Equations via Laguerre Transform Approach
اسم المؤلف:
غصون سعيد عبد محمد
اسم المشرف:
ايمان علي حسين
الموضوع العام:
علوم الرياضيات
السنة:
2015
الموضوع الدقيق:
التحليل العددي
الدرجة:
ماجستير
الجامعة:
الجامعة المستنصرية - كلية التربية للعلوم الصرفة
اللغة:
الانكليزية
مكان الجامعة:
بغداد
الصفحات الاولى:
📎 27T1172 - p.pdf
المستخلص:
The main aim of this work is to introduce new formulae that can be used to deal with LT and to utilize them for solving different types of DEs.A new simple general formula is derived to evaluate the LT of the higher derivatives of a variable. The new formula is easily modeled by a computer program, and there is no need for tedious operations of successive integration by part, as in the conventional method.This work proposes a method utilizing LT to solve ODE's (linear and nonlinear, homogeneous or inhomogeneous, boundary or initial value problems), which is explained and implemented in different examples. The results are in a good agreement with the analytical solution.Two other new methods are proposed, utilizing LT to solve PDE's with one spatial dimension. The two methods are explained and implemented in different examples, and the results show a good agreement with the analytical solutions.Another new method, utilizing LT, is proposed to solve PDE's with two spatial dimensions. The method is implemented to solve heat equation with two spatial dimensions and the results show a good agreement with that of finite difference solution. The method is also modified to achieve image smoothing as a global smoothing technique. The new image smoothing technique is compared with a finite difference technique for image smoothing, which is a local smoothing technique. The results of the proposed new technique show better smoothing (less fogy) with an expenditure of a long execution time.Finally, it is worth to mention that all the programs used in this work have been coded by the MATLAB 7 system environment
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