Muhammad Abbas

Muhammad Yaseen, Muhammad Abbas

In this paper, an efficient numerical technique for the time-fractional telegraph equation is proposed. The aim of this paper is to use a relatively new type of B-spline called the cubic trigonometric B-splines for the proposed scheme. This technique is based on finite difference formulation for the Caputo time-fractional derivative and cubic trigonometric B-splines based technique for the derivatives in space. A stability analysis of the scheme is set up to affirm that the errors do not amplify. Computational experiments are carried out in addition to verify the theoretical analysis. Numerical results are compared with some existing techniques and it is concluded that the present scheme is more accurate and effective.

Ali Nawaz, Attique Ur Rehman, Muhammad Abbas

Software testing is one of the important ways to ensure the quality of software. It is found that testing cost more than 50% of overall project cost. Effective and efficient software testing utilizes the minimum resources of software. Therefore, it is important to construct the procedure which is not only able to perform the efficient testing but also minimizes the utilization of project resources. The goal of software testing is to find maximum defects in the software system. More the defects found in the software ensure more efficiency is the software testing Different techniques have been proposed to detect the defects in software and to utilize the resources and achieve good results. As world is continuously moving toward data driven approach for making important decision. Therefore, in this research paper we performed the machine learning analysis on the publicly available datasets and tried to achieve the maximum accuracy. The major focus of the paper is to apply different machine learning techniques on the datasets and find out which technique produce efficient result. Particularly, we proposed an ensemble learning models and perform comparative analysis among KNN, Decision tree, SVM and Naïve Bayes on different datasets and it is demonstrated that performance of Ensemble method is more than other methods in term of accuracy, precision, recall and F1-score. The classification accuracy of ensemble model trained on CM1 is 98.56%, classification accuracy of ensemble model trained on KM2 is 98.18% similarly, the classification accuracy of ensemble learning model trained on PC1 is 99.27%. This reveals that Ensemble is more efficient method for making the defect prediction as compared other techniques.

Muhammad Abbas

This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space discretization is achieved by means of non polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.

Muhammad Yaseen, Muhammad Abbas

This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The method is proved to be globally unconditionally stable. To measure the accuracy of the solution, a convergence analysis is also provided. A convergence analysis is Computational experiments are performed to further establish the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveal that the proposed scheme is quite accurate and effective.

Muhammad Abbas

In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis of the scheme is conducted to confirm that the scheme does not amplify errors. Computational experiments are also performed to further establish the accuracy and validity of the proposed scheme. The results obtained are compared with a finite difference schemes based on the Hermite formula and radial basis functions. It is found that our numerical approach performs superior to the existing methods due to its simple implementation, straight forward interpolation and very less computational cost.

Tahir Nazir, Muhammad Abbas, Ahmad Izani Md. Ismail et al.

This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function in the space dimension, with a weighted scheme. The scheme is shown to be unconditionally stable for a range of values using the von Neumann (Fourier) method. Several test problems are presented to confirm the accuracy of the new scheme and to show the performance of trigonometric basis functions. The proposed scheme is also computationally economical and can be used to solve complex problems. The numerical results are found to be in good agreement with known exact solutions and also with earlier studies.