Anwar Zeb - Academia.edu (original) (raw)

Papers by Anwar Zeb

Research paper thumbnail of Solution Of An Inverse Stokes Problem Using Interior Data

WIT transactions on modelling and simulation, Aug 22, 2000

Research paper thumbnail of Solution Of The Cauchy Problem For The InharmonicEquation

WIT transactions on modelling and simulation, 1970

The boundary element method is applied to discretise numerically the Cauchy problem for the bihar... more The boundary element method is applied to discretise numerically the Cauchy problem for the biharmonic equation which arises in slow viscous flow problems. The resulting ill-conditioned system of linear equations is solved using the least squares and the minimal energy methods. The numerical solution is compared with a known analytical solution and it is shown that the least squares method is unstable but the minimal energy method is stable.

Research paper thumbnail of Cauchy Problem For The Biharmonic EquationSolved Using The Regularization Method

WIT transactions on modelling and simulation, May 14, 1998

The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the b... more The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the biharmonic equation which involves over-and underspecified boundary portions of the solution domain. The resulting ill-conditioned system of linear equations is solved using the regularization method. It is shown that the regularization method performs better than the minimal energy method in the case of the biharmonic equation, unlike the Laplace equation where the minimal energy method is more efficient. Moreover, the stability of the numerical solution obtained by the regularization method is also investigated.

Research paper thumbnail of The Method of Fundamental Solutions for an Inverse Internal Boundary Value Problem for the Biharmonic Equation

International Journal of Computational Methods, Dec 1, 2009

Research paper thumbnail of The boundary element method for the solution of Stokes equations in two-dimensional domains

Engineering Analysis With Boundary Elements, Dec 1, 1998

A boundary element method for the solution of Stokes equations governing creeping flow or Stokes ... more A boundary element method for the solution of Stokes equations governing creeping flow or Stokes flow in the interior of an arbitrary twodimensional domain is presented. A procedure for introducing pressure data on the boundary of the domain is also included and the integral coefficients of the resulting linear algebraic equations are evaluated analytically. Calculations are performed in a circular domain using a variety of different boundary conditions, including a combination of the fluid velocity and the pressure. Results are presented both on the boundary and inside the solution domain in order to illustrate that the boundary element method developed here provides an efficient technique, in terms of accuracy and convergence, to investigate Stokes flow numerically.

Research paper thumbnail of A comparison of different methods to solve inverse biharmonic boundary value problems

International Journal for Numerical Methods in Engineering, Aug 30, 1999

ABSTRACT

Research paper thumbnail of An inverse Stokes problem using interior pressure data

Engineering Analysis With Boundary Elements, Oct 1, 2002

An inverse boundary value problem associated to the Stokes equations in a domain of two dimension... more An inverse boundary value problem associated to the Stokes equations in a domain of two dimensions is considered. This problem requires the determination of the unspecified surface fluid velocity, or one of its components, over a part of its boundary by introducing extra interior pressure measurements. The problem is discretised numerically using the boundary element method (BEM) and the resulting ill-conditioned system of linear algebraic equations is solved using the Tikhonov regularisation method, with the choice of the regularisation parameter based on the L-curve criterion. The numerical technique is validated for some test examples with known analytical solutions. The accuracy of the numerical solutions is checked by comparison with their corresponding exact values and an investigation into stability of the numerical solution is undertaken by the addition of random noise into the interior pressure measurements. It is shown that the BEM provides a stable numerical solution of the Stokes problem which converges to the exact solution as the magnitude of error in the interior data decreases.

Research paper thumbnail of The method of fundamental solutions for a biharmonic inverse boundary determination problem

Computational Mechanics, Feb 5, 2008

In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation i... more In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation is investigated. This problem consists of determining an unknown boundary portion of a solution domain by using additional data on the remaining known part of the boundary. The method of fundamental solutions (MFS), in combination with the Tikhonov zeroth order regularization technique, are employed. It is shown that the MFS regularization numerical technique produces a stable and accurate numerical solution for an optimal choice of the regularization parameter. Keywords Biharmonic equation • Inverse problem • Boundary determination • Method of fundamental solutions • Regularization A. Zeb on study leave visiting the University of Leeds.

Research paper thumbnail of A numerical method for an inverse biharmonic problem

Inverse Problems in Engineering, Oct 1, 1999

... Anal., 4, 147. [3] Zeb, A., Elliott, L., Ingham, DB and Lesnic, D. (1997). Solution of the Ca... more ... Anal., 4, 147. [3] Zeb, A., Elliott, L., Ingham, DB and Lesnic, D. (1997). Solution of the Cauchy problem for the biharmonic equation, In: Boundary Elements XZX, (Eds. ... Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review, 34, 561. [12] Vogel, CR (1996). ...

Research paper thumbnail of Detectable sensation of a stochastic smoking model

Open Mathematics, 2020

This paper is related to the stochastic smoking model for the purpose of creating the effects of ... more This paper is related to the stochastic smoking model for the purpose of creating the effects of smoking that are not observed in deterministic form. First, formulation of the stochastic model is presented. Then the sufficient conditions for extinction and persistence are determined. Furthermore, the threshold of the proposed stochastic model is discussed, when noises are small or large. Finally, the numerical simulations are shown graphically with the software MATLAB.

Research paper thumbnail of Boundary element two-dimensional solution of an inverse Stokes problem

Engineering Analysis with Boundary Elements, 2000

This paper considers an inverse boundary value problem associated to the Stokes equations. The de... more This paper considers an inverse boundary value problem associated to the Stokes equations. The determination of the under-specified boundary values of the normal fluid velocity is made possible by utilising within the analysis additional pressure measurements, which are available from elsewhere on the boundary. The inverse boundary value Stokes problem has been numerically discretised using a boundary element method (BEM).

Research paper thumbnail of Comparative in-vitro anti-inflammatory, anticholinesterase and antidiabetic evaluation: computational and kinetic assessment of succinimides cyano-acetate derivatives

This research was planned to synthesize cyano-acetate derivatives of succinimide and evaluate its... more This research was planned to synthesize cyano-acetate derivatives of succinimide and evaluate its comparative biological efficacy as anti-inflammatory, anti-cholinesterase and anti-diabetic, which was further validated by molecular docking studies. The three cyano-acetate derivatives of succinimide including compound 23 Methyl 2-cyano-2-(2,5-dioxopyrrolidin-3-yl)acetate, compound 31 Methyl 2-cyano-2-(1-methyl-2,5-dioxopyrrolidin-3-yl)acetate and compound 44 Methyl 2-cyano-2-(1-ethyl-2,5dioxopyrrolidin-3-yl) acetate were synthesized. The mentioned compounds were checked for in vitro anti-inflammatory, anti-cholinesterase and anti-diabetic (a-amylase inhibition) activity. To validate the in vitro results, computational studies were carried out using molecular operating environment to analyse the BE, i.e. binding energies of all synthesized compounds against the respective enzymes. The Compounds 23, 31, 44 exhibited anti-inflammatory via inhibiting COX-2 (IC 50 value of 204.08, 68.60 and 50.93 mM, respectively), COX-1 (IC 50 value of 287, 185, and 143 mM, respectively) and 5-LOX (IC 50 value of 138, 50.76 and 20, 87 mM respectively). They exhibited choline-mimetic potential, such as compound 23, 31 and 44 inhibited AChE enzyme (IC 50 value of 240, 174, and 134 mM, respectively) and BChE enzyme (IC 50 value of 203, 134 and 97 mM, respectively). The Compounds 23, 31, 44 exhibited anti-diabetic effect via inhibiting a-amylase enzyme (IC 50 values of 250, 106 and 60 mM, respectively). Molecular docking studies revealed that the synthesized compounds have good binding affinity in the binding pockets of AChE, BChE, COX-2, 5-LOX and a-amylase enzyme and showed high binding energies. The synthesized succinimide derivatives, i.e. compound 23, 31, 44 showed marked inhibitory activities against cyclooxygenase, lipoxygenase, a-amylase and cholinesterase enzymes. Among these three, compound 44 and 31 showed strong anti-inflammatory and anti-diabetic activity while they displayed moderate anti-cholinesterase activity supported by molecular docking results.

Research paper thumbnail of Solution Of An Inverse Stokes Problem Using Interior Data

WIT transactions on modelling and simulation, Aug 22, 2000

Research paper thumbnail of Solution Of The Cauchy Problem For The InharmonicEquation

WIT transactions on modelling and simulation, 1970

The boundary element method is applied to discretise numerically the Cauchy problem for the bihar... more The boundary element method is applied to discretise numerically the Cauchy problem for the biharmonic equation which arises in slow viscous flow problems. The resulting ill-conditioned system of linear equations is solved using the least squares and the minimal energy methods. The numerical solution is compared with a known analytical solution and it is shown that the least squares method is unstable but the minimal energy method is stable.

Research paper thumbnail of Cauchy Problem For The Biharmonic EquationSolved Using The Regularization Method

WIT transactions on modelling and simulation, May 14, 1998

The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the b... more The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the biharmonic equation which involves over-and underspecified boundary portions of the solution domain. The resulting ill-conditioned system of linear equations is solved using the regularization method. It is shown that the regularization method performs better than the minimal energy method in the case of the biharmonic equation, unlike the Laplace equation where the minimal energy method is more efficient. Moreover, the stability of the numerical solution obtained by the regularization method is also investigated.

Research paper thumbnail of The Method of Fundamental Solutions for an Inverse Internal Boundary Value Problem for the Biharmonic Equation

International Journal of Computational Methods, Dec 1, 2009

Research paper thumbnail of The boundary element method for the solution of Stokes equations in two-dimensional domains

Engineering Analysis With Boundary Elements, Dec 1, 1998

A boundary element method for the solution of Stokes equations governing creeping flow or Stokes ... more A boundary element method for the solution of Stokes equations governing creeping flow or Stokes flow in the interior of an arbitrary twodimensional domain is presented. A procedure for introducing pressure data on the boundary of the domain is also included and the integral coefficients of the resulting linear algebraic equations are evaluated analytically. Calculations are performed in a circular domain using a variety of different boundary conditions, including a combination of the fluid velocity and the pressure. Results are presented both on the boundary and inside the solution domain in order to illustrate that the boundary element method developed here provides an efficient technique, in terms of accuracy and convergence, to investigate Stokes flow numerically.

Research paper thumbnail of A comparison of different methods to solve inverse biharmonic boundary value problems

International Journal for Numerical Methods in Engineering, Aug 30, 1999

ABSTRACT

Research paper thumbnail of An inverse Stokes problem using interior pressure data

Engineering Analysis With Boundary Elements, Oct 1, 2002

An inverse boundary value problem associated to the Stokes equations in a domain of two dimension... more An inverse boundary value problem associated to the Stokes equations in a domain of two dimensions is considered. This problem requires the determination of the unspecified surface fluid velocity, or one of its components, over a part of its boundary by introducing extra interior pressure measurements. The problem is discretised numerically using the boundary element method (BEM) and the resulting ill-conditioned system of linear algebraic equations is solved using the Tikhonov regularisation method, with the choice of the regularisation parameter based on the L-curve criterion. The numerical technique is validated for some test examples with known analytical solutions. The accuracy of the numerical solutions is checked by comparison with their corresponding exact values and an investigation into stability of the numerical solution is undertaken by the addition of random noise into the interior pressure measurements. It is shown that the BEM provides a stable numerical solution of the Stokes problem which converges to the exact solution as the magnitude of error in the interior data decreases.

Research paper thumbnail of The method of fundamental solutions for a biharmonic inverse boundary determination problem

Computational Mechanics, Feb 5, 2008

In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation i... more In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation is investigated. This problem consists of determining an unknown boundary portion of a solution domain by using additional data on the remaining known part of the boundary. The method of fundamental solutions (MFS), in combination with the Tikhonov zeroth order regularization technique, are employed. It is shown that the MFS regularization numerical technique produces a stable and accurate numerical solution for an optimal choice of the regularization parameter. Keywords Biharmonic equation • Inverse problem • Boundary determination • Method of fundamental solutions • Regularization A. Zeb on study leave visiting the University of Leeds.

Research paper thumbnail of A numerical method for an inverse biharmonic problem

Inverse Problems in Engineering, Oct 1, 1999

... Anal., 4, 147. [3] Zeb, A., Elliott, L., Ingham, DB and Lesnic, D. (1997). Solution of the Ca... more ... Anal., 4, 147. [3] Zeb, A., Elliott, L., Ingham, DB and Lesnic, D. (1997). Solution of the Cauchy problem for the biharmonic equation, In: Boundary Elements XZX, (Eds. ... Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review, 34, 561. [12] Vogel, CR (1996). ...

Research paper thumbnail of Detectable sensation of a stochastic smoking model

Open Mathematics, 2020

This paper is related to the stochastic smoking model for the purpose of creating the effects of ... more This paper is related to the stochastic smoking model for the purpose of creating the effects of smoking that are not observed in deterministic form. First, formulation of the stochastic model is presented. Then the sufficient conditions for extinction and persistence are determined. Furthermore, the threshold of the proposed stochastic model is discussed, when noises are small or large. Finally, the numerical simulations are shown graphically with the software MATLAB.

Research paper thumbnail of Boundary element two-dimensional solution of an inverse Stokes problem

Engineering Analysis with Boundary Elements, 2000

This paper considers an inverse boundary value problem associated to the Stokes equations. The de... more This paper considers an inverse boundary value problem associated to the Stokes equations. The determination of the under-specified boundary values of the normal fluid velocity is made possible by utilising within the analysis additional pressure measurements, which are available from elsewhere on the boundary. The inverse boundary value Stokes problem has been numerically discretised using a boundary element method (BEM).

Research paper thumbnail of Comparative in-vitro anti-inflammatory, anticholinesterase and antidiabetic evaluation: computational and kinetic assessment of succinimides cyano-acetate derivatives

This research was planned to synthesize cyano-acetate derivatives of succinimide and evaluate its... more This research was planned to synthesize cyano-acetate derivatives of succinimide and evaluate its comparative biological efficacy as anti-inflammatory, anti-cholinesterase and anti-diabetic, which was further validated by molecular docking studies. The three cyano-acetate derivatives of succinimide including compound 23 Methyl 2-cyano-2-(2,5-dioxopyrrolidin-3-yl)acetate, compound 31 Methyl 2-cyano-2-(1-methyl-2,5-dioxopyrrolidin-3-yl)acetate and compound 44 Methyl 2-cyano-2-(1-ethyl-2,5dioxopyrrolidin-3-yl) acetate were synthesized. The mentioned compounds were checked for in vitro anti-inflammatory, anti-cholinesterase and anti-diabetic (a-amylase inhibition) activity. To validate the in vitro results, computational studies were carried out using molecular operating environment to analyse the BE, i.e. binding energies of all synthesized compounds against the respective enzymes. The Compounds 23, 31, 44 exhibited anti-inflammatory via inhibiting COX-2 (IC 50 value of 204.08, 68.60 and 50.93 mM, respectively), COX-1 (IC 50 value of 287, 185, and 143 mM, respectively) and 5-LOX (IC 50 value of 138, 50.76 and 20, 87 mM respectively). They exhibited choline-mimetic potential, such as compound 23, 31 and 44 inhibited AChE enzyme (IC 50 value of 240, 174, and 134 mM, respectively) and BChE enzyme (IC 50 value of 203, 134 and 97 mM, respectively). The Compounds 23, 31, 44 exhibited anti-diabetic effect via inhibiting a-amylase enzyme (IC 50 values of 250, 106 and 60 mM, respectively). Molecular docking studies revealed that the synthesized compounds have good binding affinity in the binding pockets of AChE, BChE, COX-2, 5-LOX and a-amylase enzyme and showed high binding energies. The synthesized succinimide derivatives, i.e. compound 23, 31, 44 showed marked inhibitory activities against cyclooxygenase, lipoxygenase, a-amylase and cholinesterase enzymes. Among these three, compound 44 and 31 showed strong anti-inflammatory and anti-diabetic activity while they displayed moderate anti-cholinesterase activity supported by molecular docking results.