Harinakshi Karkera^a , Nagaraj N. Katagi^a,† , Ramesh B. Kudenatti^b

Frontiers in Heat and Mass Transfer, Vol.18, pp. 1-10, 2022, DOI:10.5098/hmt.18.41

Abstract In this paper, we study the characteristics of laminar boundary-layer flow of a viscous incompressible fluid over a moving wedge. The transformed boundary-layer equation given by the Falkner-Skan equation is solved by an efficient easy-to-use approximate method based on uniform Haar wavelets in conjunction with quasilinearization and collocation approach. The residual and error estimates are computed to confirm the validity of the obtained results. A meaningful comparison between the present solutions with existing numerical results in the literature is carried out to highlight the benefits and efficiency of proposed method. Furthermore, the influence of variable pressure gradient and the wedge… More >

Ju E Yang, Qiya Hu, Dehao Yu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 71-72, 2011, DOI:10.3970/icces.2011.016.071

Abstract In this paper, based on the natural boundary reduction method advanced bu Feng and Yu, we are concerned with a domain decomposition method with nonmatching grids for a certain nonlinear interface problem in unbounded domains. We first discuss a new coupling of finite element and boundary element by adding an auxiliary circle. Then we use a dual basis multipier on the interface to provide the numerical analysis with nonmatching grids. Finally, we give some numerical examples further to confirm our theoretical results. More >

Chein-Shan Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 55-84, 2008, DOI:10.3970/icces.2008.005.055

Abstract The present paper provides a Lie-group shooting method for the numerical solutions of second-order nonlinear boundary value problems exhibiting multiple solutions. It aims to find all solutions as easy as possible. The boundary conditions considered are classified into four types, namely the Dirichlet, the first Robin, the second Robin and the Neumann. The two Robin type problems are transformed into a canonical one by using the technique of symmetric extension of the governing equations. The Lie-group shooting method is very effective to search unknown initial condition through a weighting factor r(0,1). Furthermore, the closed-form solutions are derived to calculate the… More >

S.A. Khuri¹, A. Sayfy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 81-96, 2014, DOI:10.3970/cmes.2014.101.081

Abstract In this article, we introduce a numerical scheme to solve a class of nonlinear two-point BVPs on a semi-infinite domain that arise in engineering applications and the physical sciences. The strategy is based on replacing the boundary condition at infinity by an asymptotic boundary condition (ABC) specified over a finite interval that approaches the given value at infinity. Then, the problem complimented with the resulting ABC is solved using a fourth order spline collocation approach constructed over uniform meshes on the truncated domain. A number of test examples are considered to confirm the accuracy, efficient treatment of the boundary condition… More >

Xiaojing Liu¹, Jizeng Wang^1,2, Youhe Zhou^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 493-505, 2013, DOI:10.3970/cmes.2013.092.493

Abstract By combining techniques of boundary extension and Coiflet-type wavelet expansion, an approximation scheme for a function defined on a two-dimensional bounded space is proposed. In this wavelet approximation, each expansion coefficient can be directly obtained by a single-point sampling of the function. And the boundary values and derivatives of the bounded function can be embedded in the modified wavelet basis. Based on this approximation scheme, a modified wavelet Galerkin method is developed for solving two-dimensional nonlinear boundary value problems, in which the interpolating property makes the solution of such strong nonlinear problems very effective and accurate. As an example, we… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 355-386, 2012, DOI:10.3970/cmes.2012.087.355

Abstract The paper presents a new meshless numerical technique for solving nonlinear Poisson-type equation ∇²u = f (x) + F(u,x) for x ∈ R^d, d =1,2,3. We assume that the nonlinear term can be represented as a linear combination of basis functions F(u,x) = ∑_m^Mq_mφ_m. We use the basis functions φ_m of three types: the the monomials, the trigonometric functions and the multiquadric radial basis functions. For basis functions φ_m of each kind there exist particular solutions of the equation ∇²ϕ_m = φ_m in an analytic form. This permits to write the approximate solution in the form u_M = u_f… More >