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 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 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 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 +∑_m^Mq_mΦ_m, where Φ_m… More >