Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations
المؤلف
المصدر
Discrete Dynamics in Nature and Society
العدد
المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-19، 19ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2020-05-17
دولة النشر
مصر
عدد الصفحات
19
التخصصات الرئيسية
الملخص EN
This work presents the novel continuum-cancellation Leal-method (CCLM) for the approximation of nonlinear differential equations.
CCLM obtains accurate approximate analytical solutions resorting to a process that involves the continuum cancellation (CC) of the residual error of multiple selected points; such CC process occurs during the successive derivatives of the differential equation resulting in an accuracy increase of the inner region of the CC-points and, thus, extends the domain of convergence and accuracy.
Users of CCLM can propose their own trial functions to construct the approximation as long as they are continuous in the CC-points, that is, it can be polynomials, exponentials, and rational polynomials, among others.
In addition, we show how the process to obtain the approximations is straightforward and simple to achieve and capable to generate compact, and easy, computable expressions.
A convergence control is proposed with the aim to establish a solid scheme to obtain optimal CCLM approximations.
Furthermore, we present the application of CCLM in several examples: Thomas–Fermi singular equation for the neutral atom, magnetohydrodynamic flow of blood in a porous channel singular boundary-valued problem, and a system of initial condition differential equations to model the dynamics of cocaine consumption in Spain.
We present a computational convergence study for the proposed approximations resulting in a tendency of the RMS error to zero as the approximation order increases for all case studies.
In addition, a computation time analysis (using Fortran) for the proposed approximations presents average times from 3.5 nanoseconds to 7 nanoseconds for all the case studies.
Thence, CCML approximations can be used for intensive computing simulations.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Vazquez-Leal, Hector. 2020. Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1153118
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Vazquez-Leal, Hector. Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-19.
https://search.emarefa.net/detail/BIM-1153118
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Vazquez-Leal, Hector. Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1153118
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1153118
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر