Keywords: Nonlinear equations; Iterative methods; Optimal order of convergence; 02.60.Jh; 02.60.Lj;
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Keywords: Fractional derivative; Generalized differential transform; Boundary value problem; Nonlinear differential equation; 02.60.Cb; 02.60.Lj; 05.45.-a;
Abundant soliton solutions for the Kundu–Eckhaus equation via tan(ϕ(ξ))-expansion method
Keywords: 02.60.Lj; 02.70.Wz; 02.90.+p; 04.30.NkImproved tan(Φ(ξ)/2)tanΦ(ξ)/2-expansion method; Kundu–Eckhaus equation; Solitons; Kink; Periodic and rational solutions
Caputo derivatives of fractional variable order: Numerical approximations
Keywords: Fractional calculus; Fractional variable order; Fractional differential equations; Approximation methods33F05; 35R1102.30.Gp; 02.60.Lj
Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet
Keywords: 02.60.Cb; 02.60.Lj; 44.05.+e; 47.15.CbAdomian method; Padé approximants; MHD; Boundary layer
On the approximate solution to an initial boundary valued problem for the Cahn–Hilliard equation
Keywords: 02.60.-x; 02.60.Lj; 05.70.Fh; 64.75.OpAdomian polynomials; Fourier Method; Cahn–Hilliard equation; Pattern formation; Initial homogeneous boundary valued problem
Solution of a laminar boundary layer flow via a numerical method
Keywords: 47.15.Cb; 02.60.Lj; 02.70.Hm; 02.70.JnLaminar boundary layer; Blasius equation; Rational Chebyshev functions; Collocation method; Nonlinear ODE; Semi-infinite interval; Spectral methods
Some new uses of the ηm(Z)ηm(Z) functions
Keywords: 02.60.Lj; 02.70.Wz; 03.65.Geηmηm set of functions; Exponential fitting; Approximation formulae
Tension spline approach for the numerical solution of nonlinear Klein–Gordon equation
Keywords: 02.30.Jr; 02.60.Lj; 02.60.-x; 02.60.Cb; 02.70.BfNon-polynomial spline; Finite difference; Klein–Gordon equation; Stability analysis; Convergence
The monotonic Quartic Spline Method (QSM) for conservative transport problems
Keywords: 02.60.Lj; 02.70.Bf; 47.11.Df; 92.30.EfAdvection; Conservation; Monotonicity; PPM; PSM; Remapping
Solution of the MHD Falkner-Skan flow by Hankel-Padé method
Keywords: 02.30.Hq; 02.30.Mv; 02.60.Lj; 47.15.Cb; Boundary layer flow; Magnetohydrodynamic (MHD) flow; Padé approximation; Hankel-Padé method; Crocco's transformation;
A computationally efficient scheme for the non-linear diffusion equation
Keywords: 02.60.Lj; 47.11.-j; 47.27.Tb; 92.60.Hk; Numerics; Diffusion; Nonlinear instability; Atmospheric models;
Two new solutions to the third-order symplectic integration method
Keywords: 02.60.Lj; 02.30.Hq; 02.60.Jh; 45.10.-bSymplectic integrator; Ruth's method; Hamiltonian system; Computational acoustics
Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation
Keywords: 02.60.2x; 02.60.Cb; 02.60.Lj; 02.70.-c; 02.70.BfSchrödinger equation; One step method; Obrechkoff method; Multi precision
Bit propagation in (2+1)-dimensional systems of coupled sine-Gordon equations
Keywords: 02.60.Lj; 45.10.âb; 63.20.Pw; (2+1)-Dimensional sine-Gordon equation; Discrete nonlinear systems; Nonlinear supratransmission; Intrinsic nonlinear modes;
Persistence of travelling waves in a generalized Fisher equation
Keywords: 02.30.Jr; 02.60.Lj; Generalized Fisher equation; Travelling waves; Persistence; Fenichel's theory;
An efficient analytical approach for solving fourth order boundary value problems
Keywords: 02.60.Lj; 04.25.Nx; 02.70.Wz; 02.60.Cb; Homotopy analysis method; Boundary value problem; Analytical solution; Numerical solution; Symbolic computation;
The homotopy analysis method for multiple solutions of nonlinear boundary value problems
Keywords: 02.30.Hq; 02.60.Lj; 82.20.NKReaction-diffusion model; Dual solutions; Homotopy analysis method; Base functions; Auxiliary parameter; Initial approximation
Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes
Keywords: 02.60.Lj; 44.25.+f; 47.15.Cb; 47.55.âP; 47.56.+r; 51.20.+d; Natural convection; Soret and Dufour effects; Mass transfer; Porous medium; Variable heat flux; Numerical analysis;
Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects
Keywords: 02.60.Lj; 47.55.Mh; 47.15.Cb; 47.70Magnetohydrodynamic thermal convection flow; Mass transfer; Stretching surface; Materials processing; Porous medium; Soret number; Dufour number; Buoyancy; Nusselt number; Sherwood number; Numerical analysis
Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations
Keywords: 34C10; 39A1002.30.Hq; 02.30.Ks; 02.60.Lj; 02.70.BfDynamic equation; Time scale; Nonlinear; Superlinear; Sublinear; Oscillation
Approximate analytical solution for MHD stagnation-point flow in porous media
Keywords: 02.60.Lj; 44.05.+e; 44.30.+vHeat transfer; Boundary layer; Magnetohydrodynamic; Stagnation flow; Porous media; Adomian decomposition method
Efficient computation of high index Sturm–Liouville eigenvalues for problems in physics
Keywords: 02.30.Hq; 02.60.Lj; 02.60.Jh; 03.65.-wSturm–Liouville; Schrödinger; Eigenvalue; Shooting
On exact solutions for thin film flows of a micropolar fluid
Keywords: 02.60.Lj; 44.05.+e; 47.50.−dMicropolar fluid; Thin film flow; Exact solutions
Homotopy analysis method for singular IVPs of Emden–Fowler type
Keywords: 02.60.Lj; 02.30.Hq; 02.30.Mv; 02.60.CbHomotopy analysis method; Lane–Emden equation; Emden–Fowler equations; Singular IVPs
Multisymplectic numerical method for the regularized long-wave equation
Keywords: 02.60.Cb; 02.60.Lj; 02.60.Gf; 05.45.YvThe regularized long-wave equation; Multisymplectic structure; Preissman scheme; Backward error analysis; Solitons; Undular bore
An implicit four-step computational method in the study on the effects of damping in a modified αα-Fermi–Pasta–Ulam medium
Keywords: 02.60.Lj; 02.70.Bf; 45.10.-bFermi–Pasta–Ulam media; Discrete Fermi–Pasta–Ulam chains; Finite-difference schemes; Energy schemes; Nonstandard methods; Nonlinear problem; Consistency properties; Energy analysis; Damped systems; Anharmonic oscillators
Modified homotopy analysis method for solving systems of second-order BVPs
Keywords: 02.60.Lj; 02.30.Hq; 02.30.Mv; 02.60.CbBoundary-value problems; Homotopy analysis method; Modified homotopy analysis method
On a new reliable modification of homotopy analysis method
Keywords: 02.60.Lj; 02.30.Hq; 02.30.Mv; 02.60.CbHomotopy analysis method; Modified homotopy analysis method; Non-linear equations
ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm–Liouville problem
Keywords: 02.60.Lj; 31.15.Ja; 32.80.FbEigenvalue problems; Kantorovich method; Finite element method; Ordinary differential equations; High-order accuracy approximations
Dynamical models of molecular chains and efficient integration algorithms
Keywords: 45.40.−f; 36.20.Fz; 02.60.Lj; 07.05.TpRigidity constraints; Hard springs; Runge–Kutta; Flipping rule; Molecular chains
Magnus’ expansion for time-periodic systems: Parameter-dependent approximations
Keywords: 02.30.Hq; 02.30.Mv; 02.60.Lj; 02.70.WzMagnus expansion; Time-periodic systems; Chebyshev polynomials
Fortran programs for the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap
Keywords: 02.60.Lj; 02.60.Jh; 02.60.Cb; 03.75.-bBose–Einstein condensate; Gross–Pitaevskii equation; Split-step Crank–Nicolson scheme; Real- and imaginary-time propagation; Fortran program; Partial differential equation
A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes
Keywords: 02.60.Ed; 02.60.Lj; 47.10.ad; 92.60.hkMoving least squares; Interpolation; Singularities; Convection; Diffusion; Navier–Stokes
Approximate solutions of singular two-point BVPs by modified homotopy analysis method
Keywords: 02.60.Lj; 02.30.Hq; 02.30.Mv; 02.60.CbModified homotopy analysis method; Singular two-point boundary value problems; Series solutions
Comparison between analytical and numeric determination of the interface curvature during dewetted Bridgman crystal growth
Keywords: 02.60.Cb; 02.60.Lj; 02.70.Dh; 68.08.âp; A1. Computer simulation; A1. Heat transfer; A1. Interfaces;
Effect of buoyancy and Marangoni forces on the dopant distribution in a single crystal fiber grown from the melt by edge-defined film-fed growth (EFG) method
Keywords: 02.60.Cb; 02.60.Lj; 47.20.Bp; 47.20.Dr; 68.08.âp; 68.35.Dv; 71.20.Nr; A1. Computer simulation; A1. Fluid flows; A1. Mass transfer; A2. Edge-defined film-fed growth; B1. Rare earth compounds;
An efficient shooting method for fiber amplifiers and lasers
Keywords: 42.60.Da; 02.60.Lj; 42.65.Yj; 42.55.WdShooting method; Raman fiber amplifier; Yb-doped double-clad fiber laser
Magnetic domain walls and the relaxation method
Keywords: 75.60.Ch; 75.70.Kw; 02.60.Cb; 02.60.Lj; Domain walls and domain structure; Domain structure; Numerical simulation; Solution of equations; Ordinary and partial differential equations; Boundary value problems;
Dependence of the meniscus shape on the pressure difference in the dewetted Bridgman process
Keywords: 02.60.Cb; 02.60.Lj; 68.08.âp; 68.08.Bc; 71.20.Nr; 74.62.Fj; A1. Computer simulation; A2. Dewetted Bridgman technique; A2. Growth from the melt; A2. Single crystal growth; B1. Antimonides; B1. Gallium compounds;
On the transmission of binary bits in discrete Josephson-junction arrays
Keywords: 02.60.Lj; 63.20.Pw; 74.50.+rDiscrete Josephson-junction arrays; Nonlinear supratransmission and infratransmission; Signal propagation; Sine-Gordon equation; Localized modes
On the similarity solutions for a steady MHD equation
Keywords: 02.60.Lj; 47.15.Cb; 47.65.−dBoundary layer; Similarity solution; Third order non-linear differential equation; Boundary value problem; MHD
KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach
Keywords: 02.30.Hq; 02.60.Jh; 02.60.Lj; 03.65.Nk; 31.15.Ja; 31.15.Pf; 34.50.-s; 34.80.BmEigenvalue and multi-channel scattering problems; Kantorovich method; Finite element method; R-matrix calculations; Hyperspherical coordinates; Multi-channel adiabatic approxima
Solitary wave solutions of the modified equal width wave equation
Keywords: 02.60.Lj; 02.70.Bf; 05.45.YvMEW equation; Linearized implicit finite-difference; Solitary waves
Initial-oblique derivative problem for nonlinear parabolic systems in high dimensional domains
Keywords: 35K15; 35K20; 35K60; 02.30.Hq; 02.60.Lj; Initial-oblique derivative problem; Nonlinear parabolic systems; High dimensional domains;
Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet
Keywords: 02.60.Lj; 44.05.+e; 47.50.−dUnsteady axisymmetric flow; Heat transfer analysis; Viscous fluid; HAM solution; Stretching sheet
Sixth-order symmetric and symplectic exponentially fitted modified Runge–Kutta methods of Gauss type
Keywords: 02.60.Lj; 02.70.-c; 02.90.+pExponential fitting; Symmetry; Symplecticness; Modified RK methods; Oscillatory Hamiltonian systems
Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission
Keywords: 02.60.Lj; 02.70.Bf; 03.65.Ge; 25.85.EcTwo-dimensional Schrödinger equation; Adapted finite difference formulae; Cassini parametrization; Algebraic eigenvalue problem; Arnoldi method; Scission neutrons; Sudden approximation
Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks
Keywords: 02.60.Cb; 02.60.−c; 07.05.Mh; 02.60.Lj; 07.05.TpFeed-forward neural network; Schrodinger equation; Differential equation; Energy function; Eigenfunction; Eigenvalue
On a model of three-dimensional bursting and its parallel implementation
Keywords: 82.40.Ck; 02.60.Lj; 07.05.TpReaction–diffusion equations; Bursting; Three-dimensional model; MPI; OpenMP; PETSc; Performance representation