A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows
From MaRDI portal
Publication:3486316
DOI10.1137/1032079zbMath0705.76062OpenAlexW2015562476MaRDI QIDQ3486316
E. O. Tuck, Leonard W. Schwartz
Publication date: 1990
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/1032079
boundary conditiondrainingsurface tension forcescoating fluid-flow problemsthird- order ordinary differential equations
Nonlinear boundary value problems for ordinary differential equations (34B15) Asymptotic expansions of solutions to ordinary differential equations (34E05)
Related Items
Inverse spectral problem for the third-order differential equation ⋮ On sinc discretization and banded preconditioning for linear third-order ordinary differential equations ⋮ The effect of an axial temperature gradient on the steady motion of a large droplet in a tube ⋮ Finger Formation and Non-newtonian Fluids ⋮ Singular integral equations arising in draining and coating flows ⋮ An existence theorem for a singular third-order boundary value problem on \([0,+\infty)\) ⋮ Contact-line fingering and rivulet formation in the presence of surface contamination ⋮ The dynamics of pendant droplets on a one-dimensional surface ⋮ Numerical solutions of third-order system of boundary value problems ⋮ A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications ⋮ Symmetries, first integrals and phase planes of a third-order ordinary differential equation from thin film flow ⋮ The halting of contact lines in slender viscous films driven by gravity and surface tension gradients ⋮ The role of symmetries in solving differential equations ⋮ Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution ⋮ Existence and features of similarity solutions for non-Boussinesq gravity currents ⋮ The third-order differential equation arising in thin-film flows and relevant to Tanner's law ⋮ Numerical investigation of a third-order ODE from thin film flow ⋮ Travelling wave solutions for a thin-film equation related to the spin-coating process ⋮ Laplace pressure driven drop spreading ⋮ Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow ⋮ Unnamed Item ⋮ On the solvability of third-order three point systems of differential equations with dependence on the first derivative ⋮ Higher‐order numerical methods for third‐order non‐linear boundary value problems ⋮ On a defocusing quasilinear Schrödinger equation with singular term ⋮ Contact-line motion of shear-thinning liquids ⋮ A nonlinear eigenvalue problem from thin-film flow ⋮ Numerical Solutions of Third-Order Boundary Value Problems associated with Draining and Coating Flows ⋮ Elastic-plated gravity currents ⋮ Closed-form solution of a thermocapillary free-film problem due to Pukhnachev ⋮ Cubic splines method for a system of third-order boundary value problems ⋮ Stability of a ridge of fluid ⋮ Infinitely many nodal solutions of superlinear third order two-point boundary value problems ⋮ Existence and localization of unbounded solutions for fully nonlinear systems of jerk equations on the half-line ⋮ Upstream influence and the form of standing hydraulic jumps in liquid-layer flows on favourable slopes ⋮ Existence and uniqueness results for third-order nonlinear differential systems ⋮ Comparative study on order-reduced methods for linear third-order ordinary differential equations ⋮ Finite difference method for solving a system of third-order boundary value problems ⋮ Mathematical modelling of the motion of hard contact lenses ⋮ Solvability of generalized third-order coupled systems with two-point boundary conditions ⋮ Dynamic wetting of shear thinning fluids ⋮ On the determination of the steady film profile for a non-Newtonian thin droplet ⋮ Existence of solutions for a third-order multipoint boundary value problem with \(p\)-Laplacian ⋮ An investigation of an Emden-Fowler equation from thin film flow ⋮ Block-triangular preconditioning methods for linear third-order ordinary differential equations based on reduced-order sinc discretizations ⋮ Effects of inertia on the hydrodynamics near moving contact lines ⋮ Nonlinear dynamics and transient growth of driven contact lines ⋮ Fingering phenomena for driven coating films ⋮ Nonlinear higher-order boundary value problems describing thin viscous flows near edges ⋮ The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations ⋮ On the asymptotics of eigenvalues of a third-order differential operator ⋮ Asymmetric travelling waves for the thin film equation ⋮ Computer simulation of third‐order nonlinear singular problems arising in draining and coating flows ⋮ Theoretical and numerical results for spin coating of viscous liquids ⋮ Pattern formation in the flow of thin films down an incline: Constant flux configuration ⋮ Slowly accreting ice due to supercooled water impacting on a cold surface ⋮ A semi-infinite bubble advancing into a planar tapered channel ⋮ The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface ⋮ Parametric quintic spline solution of third-order boundary value problems ⋮ On some third order nonlinear boundary value problems: Existence, location and multiplicity results ⋮ Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation ⋮ Surface-tension- and injection-driven spreading of a thin viscous film ⋮ Solving a system of third-order boundary value problem using variational iteration method ⋮ Numerical solutions for system of third-order boundary value problems ⋮ Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving \(y(x)=f(x,y,y')\) ⋮ Mathematical modeling and numerical simulation of wave-front flow on a vertical wall with surfactant effects ⋮ Periodic behavior of a nonlinear third order vibrating system ⋮ Fingering instability on curved substrates: optimal initial film and substrate perturbations ⋮ Thin static drops with a free attachment boundary ⋮ Unnamed Item ⋮ Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves ⋮ Pressure driven disturbances on a thin viscous film ⋮ Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model ⋮ A level-set approach for simulations of flows with multiple moving contact lines with hysteresis ⋮ Stability of Newtonian and viscoelastic dynamic contact lines ⋮ Unsteady spreading of thin liquid films with small surface tension ⋮ A new integrator for special third order differential equations with application to thin film flow problem ⋮ On liquid films on an inclined plate ⋮ Asymptotic and numerical analysis of a simple model for blade coating ⋮ Linear stability analysis of a sharp-interface model for dewetting thin films ⋮ Bounded positive solutions of an iterative three-point boundary-value problem with integral boundary condtions ⋮ THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE ⋮ A two-step hybrid block method with fourth derivatives for solving third-order boundary value problems ⋮ On order-reducible sinc discretizations and block-diagonal preconditioning methods for linear third-order ordinary differential equations ⋮ Capillary ripples in thin viscous films ⋮ Similarity solutions of thin film flow driven by gravity and surface shear ⋮ Numerical solutions of third-order obstacle problems ⋮ Low-dimensional modelling of dynamics via computer algebra ⋮ Existence of positive solutions for a singular third-order two-point boundary value problem on the half-line ⋮ Surfactant-driven motion and splitting of droplets on a substrate ⋮ A smooth approximation for the solution of special non-linear third-order boundary-value problems based on non-polynomial splines ⋮ Transient growth in driven contact lines ⋮ On nontrivial traveling waves in thin film flows including contact lines ⋮ Nonpolynomial spline approach to the solution of a system of third-order boundary-value problems ⋮ An accurate block hybrid collocation method for third order ordinary differential equations ⋮ Existence of solutions for third-order \(\phi\)-Laplacian BVPs on the half-line ⋮ Spreading of viscoplastic droplets ⋮ Finite-difference method for a system of third-order boundary-value problems ⋮ A uniqueness and existence theorem for a singular third-order boundary value problem on \([0,\infty)\) ⋮ Solvability of a third-order three-point boundary value problem on a half-line ⋮ Solvability of higher-order BVPs in the half-line with unbounded nonlinearities