M. Umeshaiah¹ , M. R. Krishnamurthy² , N.G. Rudraswamy³ , B. J. Gireesha⁴, B.C. Prasannakumara^5,*

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-8, 2017, DOI:10.5098/hmt.9.4

Abstract This article presents the effect of nonlinear thermal radiation on boundary layer flow and heat transfer of Carreau fluid model over a nonlinear stretching sheet embedded in a porous medium in the presence of non-uniform heat source/sink and viscous dissipation with convective boundary condition. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations using similarity transformation, which is then solved numerically by the fourth-fifth order Runge–Kutta-Fehlberg integration scheme featuring a shooting technique. The influence of significant parameters such as power law index parameter, Stretching parameter, More >

F. Bulut^1,2, Ö. Oruç³, A. Esen³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 263-284, 2015, DOI:10.3970/cmes.2015.108.263

Abstract In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn’t use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L₂ and L_∞ error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for More >

Chia-Ming Fan^1,2, Yu-Kai Huang¹, Po-Wei Li¹, Ying-Te Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.6, pp. 491-515, 2015, DOI:10.3970/cmes.2015.105.491

Abstract In this paper, the boundary knot method (BKM) is adopted for accurately analyzing two-dimensional Stokes flows, dominated by viscous force and pressure gradient force. The Stokes flows, which denoted the flow fields with extremely viscous fluid or with very small velocity, appear in various engineering applications, such that it is very important to develop an efficient and accurate numerical method to solve the Stokes equations. The BKM, which can avoid the controversial fictitious boundary for sources, is an integral-free boundary-type meshless method and its solutions are expressed as linear combinations of nonsingular general solutions for More >

S. Saha Ray¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 231-249, 2015, DOI:10.3970/cmes.2015.105.231

Abstract In the present article, a relatively very new technique viz. Coupled Fractional Reduced Differential Transform, has been executed to attain the approximate numerical solution of the predator-prey dynamical system. The fractional derivatives are defined in the Caputo sense. Utilizing the present method we can solve many linear and nonlinear coupled fractional differential equations. The results thus obtained are compared with those of other available methods. Numerical solutions are presented graphically to show the simplicity and authenticity of the method. More >

Jinsheng Wang¹, Liqing Liu², Yiming Chen², Lechun Liu², Dayan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 69-85, 2015, DOI:10.3970/cmes.2015.104.069

Abstract The aim of this paper is to seek the numerical solution of a class of variable order fractional integral-differential equation in terms of Bernstein polynomials. The fractional derivative is described in the Caputo sense. Four kinds of operational matrixes of Bernstein polynomials are introduced and are utilized to reduce the initial equation to the solution of algebraic equations after dispersing the variable. By solving the algebraic equations, the numerical solutions are acquired. The method in general is easy to implement and yields good results. Numerical examples are provided to demonstrate the validity and applicability of More >

Baofeng Li ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 105-122, 2014, DOI:10.3970/cmes.2014.099.105

Abstract In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach. More >

Yiming Chen¹, Xiaoning Han¹, Lechun Liu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 391-405, 2014, DOI:10.3970/cmes.2014.097.391

Abstract In this paper, a class of linear system of fractional differential equations is considered. It has been solved by operational matrix of Haar wavelet method which converts the problem into algebraic equations. Moreover the convergence of the method is studied, and three numerical examples are provided to demonstrate the accuracy and efficiency. More >

Vinita Chellappan¹, S. Gopalakrishnan¹ and V. Mani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 131-174, 2014, DOI:10.3970/cmes.2014.097.131

Abstract The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly… More >

Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

Yiming Chen¹, Liqing Liu¹, Xuan Li¹ and Yannan Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 81-100, 2014, DOI:10.3970/cmes.2014.097.081

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order time fractional diffusion equation. Coimbra variable order fractional operator is adopted, as it is the most appropriate and desirable definition for physical modeling. The Coimbra variable order fractional operator can also be regarded as a Caputo-type definition. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the equation is transformed into the products of several dependent matrixes which can also be More >