MODIFIED DECOMPOSITION METHOD FOR SOLVING INITIAL AND BOUNDARY VALUE PROBLEMS USING PADE APPROXIMANTS

Noor, Muhammad Aslam,Noor, Khalida Inayat,Mohyud-Din, Syed Tauseef,Shaikh, Noor Ahmed The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

Traditional and cultural uses of medicinal plant species in the flora of Kuz Abakhel, for the treatment of various ailments

Muhammad Noor,Uddin Nisar,Khan Muhammad Khalil Ullah,Umer Muhammad,Ali Niaz,Ullah Shariat 경희대학교 융합한의과학연구소 2021 Oriental Pharmacy and Experimental Medicine Vol.21 No.3

The rural and cultural life style of indigenous people of Kuz Abakhel is urging them in touch to folk medicines for treatment of various ailments. Seventy-four plant species were documented that were used by the local people for the treatment of different ailments. These plants were commonly used as an ethno medicine against 49 major different disorders, out of which most commonly happened were; Anemia Anesthetics, unconsciousness, Anoxia etc. The principal medicinal plants with maximum used values were Aesculus indica (Wall.ex Comb) Hook.f (0.998), Ajuga bracteosa (0.996). RFC values; the maximum quoted medicinal plant species by the indigenous drivers are A. indica (RFCs = 0.999), A. bracteosa (0.996), Ajuga niponsis (0.994), Allium cepa (0.993) whereas maximum respondents %age was observed for the same plant species examined through consensus index, the (CI% = 90.84%) was for Aesculus indica and A. bracteosa. The medicinal plant species A. indica mentioned 100% for hepatitis. The diseases like. Anemia, Anesthetics and unconsciousness, Anoxia, Anti-dandruff, Antispasmodic, Arthritis, Body coldness and sexual tonic, Eye disease, Gonorrhea, Infertility, Mouth ulcer, Myiasis, Nerve tonic, Pain killer, Refrigerant, Rheumatism, Septicemia, Throat pain, Toothache, had highest FIC value due to depiction by only a single plant taxa/specie (Nt = 1). The current study exposed the significance to compose and offer a list of all the possible plants that are used in folk and ethnic medicinal practices against various ailments in the unexplored area of Kuz Abakhel and to demonstrate the important medicinal plants for future phytochemical and pharmacological research.

Efficiency of Various Nutritional Sources to Improve Physical Properties of Saline-Sodic Soil

Noor-Us-Sabah, Noor-Us-Sabah,Sarwar, Ghulam,Ibrahim, Muhammad,Tahir, Mukkram Ali,Iftikhar, Yasir,Haider, Muhammad Sajjad,Han, Kyung-Hwa,Ha, Sang-Keun,Zhang, Yong-Seon Korean Society of Soil Science and Fertilizer 2012 한국토양비료학회지 Vol.45 No.1

This study was conducted to evaluate the efficiency of various inorganic and organic materials to improve physical properties of soil. Saline sodic soil (saturation percentage = 40.36%, $EC_e=5.15dS\;m^{-1}$, $pH_s=8.70$, $SAR=18.84(m\;mol\;L^{-1})^{1/2}$, bulk density =$1.49Mg\;m^{-3}$) was collected, brought to wire house and filled in pots after laboratory analysis for various parameters. Different sources of organic nutrients like farm manure (FM), press mud, compost, poultry manure and sesbania green manure were analyzed for their chemical composition. The experiment comprised of 12 treatments replicated thrice; $T_1$: control (recommended NPK), $T_2:{\frac{1}{2}}$ recommended NPK, $T_3$: FM at 1.5% by soil weight, $T_4$: pressmud at 1.5% by soil weight, $T_5$: compost at 1.5% by soil weight, $T_6$: poultry manure at 1.5% by soil weight, $T_7$: sesbania green manure at 1.5% by soil weight, $T_8:T_2$ + FM at 0.75% by soil weight, $T_9:T_2$ + pressmud at 0.75% by soil weight, $T_{10}:T_2$ + compost at 0.75% by soil weight, $T_{11}:T_2$ + poultry manure at 0.75% by soil weight, $T_{12}:T_2$ + sesbania green manure at 0.75% by soil weight. These treatments were applied using completely randomized (CR) design and appropriate time was given to decompose these organic nutritional sources. Seeds of wheat cultivar Sahar-2006 were sown. After harvesting the wheat, soil samples were collected from each pot and analyzed for various physical properties like bulk density, porosity and saturation percentage. An improvement in physical properties (bulk density, porosity and saturation percentage) of soil was noticed with the application of various organic nutritional sources but role of compost alone ($T_5$) remained prominent.

Effects of elastic medium on buckling of microtubules due to bending and torsion

Taj, Muhammad,Hussain, Muzamal,Afsar, Muhammad A.,Safeer, Muhammad,Ahmad, Manzoor,Naeem, Muhammad N.,Badshah, Noor,Khan, Arshad,Tounsi, Abdelouahed Techno-Press 2020 Advances in concrete construction Vol.9 No.5

Microtubules buckle under bending and torsion and this property has been studied for free microtubules before using orthotropic elastic shell model. But as microtubules are embedded in other elastic filaments and it is experimentally showed that these elastic filaments affect the critical buckling moment and critical buckling torque of the microtubules. To prove that, we developed orthotropic Winkler like model and demonstrated that the critical buckling moment and critical buckling torque of the microtubules are orders of higher magnitude than those found for free microtubules. Our results show that Critical buckling moment is about 6.04 nNnm for which the corresponding curvature is about θ = 1.33 rad /㎛ for embedded MTs, and critical buckling torque is 0.9 nNnm for the angle of 1.33 rad/㎛. Our results well proved the experimental findings.

Variants of Newton's method using fifth-order quadrature formulas: Revisited

Muhammad Aslam Noor,Muhammad Waseem 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results. In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results.

Variational decomposition method for solving sixth-order boundary value problems

Muhammad A. Noor,Syed Tauseef Mohyud-Din 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable. In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

VARIATIONAL DECOMPOSITION METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS

Noor, Muhammad Aslam,Mohyud-Din, Syed Tauseef The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

RESOLVENT EQUATIONS TECHNIQUE FOR VARIATIONAL INEQUALITIES

Noor, Muhammad-Aslam 한국전산응용수학회 1997 Journal of applied mathematics & informatics Vol.4 No.2

In this paper we establish the equivalence between the general resolvent equations and variational inequalities. This equiva-lence is used to suggest and analyze a number of iterative algorithms for solving variational inclusions. We also study the convergence criteria of the iterative algorithms. Our results include several pre-viously known results as special cases.

Regularized mixed quasi equilibrium problems

MUHAMMAD ASLAM NOOR 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

SOME PROPERTIES OF NONCONVEX FUNCTIONS

MUHAMMAD ASLAM NOOR 경남대학교 기초과학연구소 2018 Nonlinear Functional Analysis and Applications Vol.23 No.3

In this paper, we introduce and study a new class of convex functions with respect to an arbitrary function, which is called the k-convex function. These functions are nonconvex functions and include the convex function and φ-convex convex as special cases. We study some properties of k-convex functions. It is shown that the minimum of k-convex functions on the k-convex sets can be characterized by a class of variational inequalities, which is called the k-directional variational inequalities. Some open problems are also suggested for future research.