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The purpose of this paper is to present a computational technique based on Newton–Cotes quadrature rule for solving fractional order differential equation.

The numerical method reduces initial value problem into a system of algebraic equations. The method presented here is also applicable to non-linear differential equations. To deal with non-linear equations, a recursive sequence of approximations is developed using quasi-linearization technique.

The method is tested on several benchmark problems from the literature. Comparison shows the supremacy of proposed method in terms of robust accuracy and swift convergence. Method can work on several similar types of problems.

It has been demonstrated that many physical systems are modelled more accurately by fractional differential equations rather than classical differential equations. Therefore, it is vital to propose some efficient numerical method. The computational technique presented in this paper is based on Newton–Cotes quadrature rule and quasi-linearization. The key feature of the method is that it works efficiently for non-linear problems.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative.

An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems.

The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples.

The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity.

Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

The purpose of this paper is to propose a method for solving nonlinear fractional partial differential equations on the semi-infinite domain and to get better and more accurate results.

The authors proposed a method by using the Chebyshev wavelets in conjunction with differential quadrature technique. The operational matrices for the method are derived, constructed and used for the solution of nonlinear fractional partial differential equations.

The operational matrices contain many zero entries, which lead to the high efficiency of the method and reasonable accuracy is achieved even with less number of grid points. The results are in good agreement with exact solutions and more accurate as compared to Haar wavelet method.

Many engineers can use the presented method for solving their nonlinear fractional models.

This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically.

The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function.

The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions.

This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans.

The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

In the present computational study, the heat transfer and two-dimensional natural convection flow of non-Newtonian power-law fluid in a tilted rectangular enclosure is examined. The left wall of enclosure is subjected to spatially varying sinusoidal temperature distribution and right wall is cooled isothermally while the upper and lower walls are retained to be adiabatic. The flow is considered to be laminar, steady and incompressible under the influence of magnetic field. The governing mass, momentum and energy equations are transformed into dimensionless form in terms of stream function, vorticity and temperature.

Then resulted highly non-linear partial differential equations are solved computationally using Galerkin finite element method.

The exhaustive flow pattern and temperature fields are displayed through streamlines and isotherm contours for various parameters, namely, Prandtl number, Rayleigh number, Hartmann number by considering different power-law index and inclination angle. The effect of inclination angle on average Nusselt number is also shown graphically. This problem observes the potential vortex flow with elliptical core. The results show that the circular strength of the vortex formed reduces as the magnetic field strength grows. As the inclination angle increases the intensity of flow field decreases while the value of average Nusselt number increases.

This study has important applications in thermal management such as cooling techniques used in buildings, nuclear reactors, heat exchangers and power generators.

In the past few years, Haar wavelet-based numerical methods have been applied successfully to solve linear and nonlinear partial differential equations. This study aims to propose a wavelet collocation method based on Haar wavelets to identify a parameter in parabolic partial differential equations (PDEs). As Haar wavelet is defined in a very simple way, implementation of the Haar wavelet method becomes easier than the other numerical methods such as finite element method and spectral method. The computational time taken by this method is very less because Haar matrices and Haar integral matrices are stored once and used for each iteration. In the case of Haar wavelet method, Dirichlet boundary conditions are incorporated automatically. Apart from this property, Haar wavelets are compactly supported orthonormal functions. These properties lead to a huge reduction in the computational cost of the method.

The aim of this paper is to reconstruct the source control parameter arises in quasilinear parabolic partial differential equation using Haar wavelet-based numerical method. Haar wavelets possess various properties, for example, compact support, orthonormality and closed form expression. The main difficulty with the Haar wavelet is its discontinuity. Therefore, this paper cannot directly use the Haar wavelet to solve partial differential equations. To handle this difficulty, this paper represents the highest-order derivative in terms of Haar wavelet series and using successive integration this study obtains the required term appearing in the problem. Taylor series expansion is used to obtain the second-order partial derivatives at collocation points.

An efficient and accurate numerical method based on Haar wavelet has been proposed for parameter identification in quasilinear parabolic partial differential equations. Numerical results are obtained from the proposed method and compared with the existing results obtained from various finite difference methods including Saulyev method. It is shown that the proposed method is superior than the conventional finite difference methods including Saulyev method in terms of accuracy and CPU time. Convergence analysis is presented to show the accuracy of the proposed method. An efficient algorithm is proposed to find the wavelet coefficients at target time.

The outcome of the paper would have a valuable role in the scientific community for several reasons. In the current scenario, the parabolic inverse problem has emerged as very important problem because of its application in many diverse fields such as tomography, chemical diffusion, thermoelectricity and control theory. In this paper, higher-order derivative is represented in terms of Haar wavelet series. In other words, we represent the solution in multiscale framework. This would enable us to understand the solution at various resolution levels. In the case of Haar wavelet, this paper can achieve a very good accuracy at very less resolution levels, which ultimately leads to huge reduction in the computational cost.

The theory of micropolar fluids was formulated by Eringen. A similarity solution is used to investigate the flow of such a fluid driven by a continuous porous plate. Continuous surfaces are surfaces such as polymer sheets or filaments continuously drawn from a dye. Within the framework of the boundary‐layer theory, similarity transformation is used for the specific case when the wall velocity varies linearly with component. A physical characteristic of the fluid is used as a perturbation parameter to obtain a first estimate solution. Using a perturbation technique, analytical solutions for large transfer rates are presented. Then, a quasilinearization is used to obtain a complete solution. Good agreement is found between solutions obtained with these different methods and with the numerical data in Hassanien and Gorla (1990).

The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions.

The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem which is followed by semi discretization for spatial direction using differential quadrature method (DQM). Semi discretization of the problem leads to a system of first order initial value problems which are followed by fully discretization using RK4 scheme. The method is analyzed for stability and convergence.

The method is illustrated and compared with existing methods via numerical experiments and it is found that the proposed method gives better accuracy and is quite easy to implement.

The new scheme is developed by using some numerical schemes. The scheme is analyzed for stability and convergence. In support of predicted theory some test examples are solved using the presented method.

This paper aims to investigate entropy generation in an incompressible magneto-micropolar nanofluid flow over a nonlinear stretching sheet. The flow is subjected to thermal radiation and viscous dissipation. The energy equation is extended by considering the impact of the Joule heating term because of an imposed magnetic field.

The flow, heat and mass transfer model are solved numerically using the spectral quasilinearization method. An analysis of the performance of this method is given.

It is found that the method is robust, converges fast and gives good accuracy. In terms of the physically significant results, the authors show that the irreversibility caused by the thermal diffusion the dominants other sources of entropy generation and the surface contributes significantly to the total irreversibility.

The flow is subjected to a combination of a buoyancy force, viscous dissipation, Joule heating and thermal radiation. The flow equations are solved numerically using the spectral quasiliearization method. The impact of a range of physical and chemical parameters on entropy generation, velocity, angular velocity, temperature and concentration profiles are determined. The current results may help in industrial applicants. The present problem has not been considered elsewhere.

This paper aims to solve the Falkner–Skan problem over an isothermal moving wedge using the combination of the quasilinearization method and the fractional order of rational Chebyshev function (FRC) collocation method on a semi-infinite domain.

The quasilinearization method converts the equation into a sequence of linear equations, and then by using the FRC collocation method, these linear equations are solved. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equation by similarity transformations.

The entropy generation and the effects of the various parameters of the problem are investigated, and various graphs for them are plotted.

Very good approximation solutions to the system of equations in the problem are obtained, and the convergence of numerical results is shown by using plots and tables.