Two Numerical ways RO (SuMM) and RO (MSuSu)) to
Evaluate triple integrals
الباحثونSafaa M. Aljassas
، Wafaa H. Hanoon and Showq Mohammed E
المجلةJournal of Physics: Conference Series
مختصر البحثThe main goal of this research to calculate the triple integrals which has continuous functions numerically by two methods are and that obtained by Romberg acceleration with two composite rules. The first rule is the Mid-point method on the first dimension X and the second dimension Y with a suggested method on the third dimension Z and, which is denoted by .The second rule is a suggested method on the first dimension X and the second dimension Y with the Mid-point method on the third dimension Z and, which is denoted by . where the number of divisions on these three dimensions is exactly the Sam. We represented two theorems with their proofs to find such rules and the correction terms (the error terms) for each of rule Therefore, we obtained high accuracy results in a relatively few sub intervals and short time.
Calculation Triple Integrals with Continuous Integrands Using
SMS and Improve Results Using Aitken’s Acceleration
الباحثونSafaa M. Aljassas ، Rehab A. Shaaban
المجلةInternational Journal of Engineering and Information Systems (IJEAIS)
مختصر البحثThe main goal of this article to calculate the triple integrals with continuous integrand numerically by using the composite rule SMS . To improve results, we used the mentioned rule with Aitken’s acceleration we called the method by we obtained high accuracy results in relatively few subintervals and short time.The main goal of this article to calculate the triple integrals with continuous integrand numerically by using the composite rule SMS . To improve results, we used the mentioned rule with Aitken’s acceleration we called the method by we obtained high accuracy results in relatively few subintervals and short time.
New Extrapolation Rule to Increase the Accuracy of Numerical Integrals Results
الباحثون
Fouad H. A. Alsharify،
Nada A. M. Al-Karamy
Safaa M. Aljassas
المجلةJour of Adv Research in Dynamical & Control Systems
مختصر البحثAbstract
This paper discusses a new method to increase the accuracy of numerical integrals results
for integrations of continuous functions or continuous functions but their derivatives are obsolete or are themselves obsolete at one end or both boundary of integration by using the error formulas associated with the Newton-Cotes integrative rules, obtained good results in improving integrality values in terms of accuracy and number of periods of fragmentation.
Driving Two Numerical Methods to Evaluate The Triple Integrals R(MSM),R(SMM) and Compare between them
الباحثونSafaa M. Aljassas، Fouad H. A. Alsharify
Nada A. M. Al - Karamy
المجلةInternational Journal of Engineering & Technology
مختصر البحثAbstract
The main objective of present research is the conclusion of two new numerical methods to evaluate the triple integrals with continuous integrands and their partial derivatives are continuous too, the first method by using Mid-point rule on the interior dimension X, Simpson's rule on the middle dimension Y and Mid-point rule on the exterior dimension Z, which denoted by the symbol MSM. The second method by using Mid-point rule on both two dimensions of interior X and middle dimension Y and Simpson's rule on the exterior dimension Z which denoted by SMM, where the number of divisions on the three dimensions are equals. We have concluded two theorems with their proves to find their rules and the correction terms that we found it and to improve the results we used Romberg acceleration which denoted by R(MSM), R(SMM) where we got high accuracy in the results by little sub-intervals relatively and short time.
Numerical Methods for Evaluation of Double integrals with Continuous Integrands
الباحثونSafaa M. Aljassas
المجلةInternational Journal of Pure and Applied Mathematics
مختصر البحثAbstract:
The main objective of this research is to introduce new numerical methods for calculating double integrations with continuous integrands. We combined between the best methods of finding approximation values for single integration, based on accelerating Romberg with a Trapezoidal rule (RT), the Mid- point rule (RM), the Simpson rule (RS) on the outer dimension Y with the Suggested method (RSu) on the inner dimension X. We call the obtained methods by RT(RSu), RM(RSu) and RS(RSu) respectively. Applying these methods on double integrals gives high accuracy results in short time and with few partial periods.
Computation of Triple Integrals with Improper Derivatives Integrands and Improper 'Numerically by Using Correction Terms Accompanying with SMS Method
الباحثونSafaa M. Aljassas
المجلةJournal of Advanced Research in Dynamical and Control Systems
مختصر البحثAbstract
The main aim of this research is to compute triple integrals with improper derivatives integrands and improper numerically, in one point of integration region using method. We presented three theorems to find the correction terms accompanying for its , by depending on the correction terms that we found it we have improved the results by using the Romberg’s acceleration method where we obtained high accuracy results in relatively few subintervals and short time.
