iterative methods for a fourth order boundary value problem abstract we consider a fourth order nonlinear ordinary differential equation together with two point boundary conditions and provide a priori error estimates on the length of the interval b a so that the picard s iterative method the approximate picard s iterative method and the quasilinear iterative method convergence to the solution of the problem

monotone convergence of iterative methods for right focal point boundary value problems abstract we provide sufficient conditions so that the picard iterative scheme for the right focal point boundary value problems converges monotonically an example which dwells upon the usefulness of this technique is also included

prime and renormalisable kneading invariants and the dynamics of expanding lorenz maps abstract we study the dynamics and kneading theory of topologically expansive piecewise increasing maps of the interval with a single discontinuity lorenz maps we characterise those maps which are locally eventually onto locally onto and neither of the above in terms of the renormalisability or otherwise of the kneading invariant we also show how the decomposition of the non wandering set is related to the renormalisability of the kneading invariant we discuss our results in the context of other authors results on similar classes of maps

the classification of topologically expansive lorenz maps we show that topologically expansive lorenz maps can be described up to topological conjugacy by their kneading invariants we also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive lorenz map a simple extension of the theorems to the case of expansive maps of the interval with multiple discontinuities is described

iterative methods for solving right focal point boundary value problems abstract we provide necessary and sufficient conditions for the existence of a solution of n th order differential equation satisfying right focal point boundary conditions for the linear problems we propose forward forward and backward backward one pass practical shooting methods which convert the boundary value problems to its equivalent initial value problems for the nonlinear problems iterative methods are discussed and a priori conditions for the convergence are obtained several examples are also illustrated

splitting words and lorenz braids abstract a canonical way to split lorenz periodic orbits is presented this allows one to recognize the braids on the lorenz template which can occur in non chaotic semi flows on this surface we first present a combinatorial version of our main result and then merely reinterpret it in topological terms

existence uniqueness and iterative methods for third order boundary value problems abstract in this paper we shall provide necessary and sufficient conditions for the existence and uniqueness of solutions of third order nonlinear differential equations satisfying three point boundary conditions for the linear case we propose a constructive method which is a variation of the method of chasing for the nonlinear problems sufficient conditions are provided to ensure the convergence of a general class of iterative methods several examples are also included

asymptotic and numerical solutions for the two dimensional solidification of a liquid half space this paper concerns the twodimensional inward solidification of a halfspace filled with molten material at its fusion temperature the temperature along half of the boundary surface is instantaneou

boundary value problems for higher order integro differential equations where r t x t x t x j t and a is a continuous operator map c l al a c ar a the function f is continuous in all of its arguments the problem l l 1 2 includes several particular cases for example the boundary value problems for the differential equations if a 0 considered in 7 8 and the references therein for the integro differential equations of the volterra type if

some flesh on the skeleton the bifurcation structure of bimodal maps abstract one of the main tools in the numerical study of two parameter families of one dimensional maps is the drawing of curves in parameter space corresponding to the existence of superstable periodic orbits we use kneading theory to describe the structure of these sets of curves for the case of maps with at most two turning points then we explain how the bifurcation structure hangs on this skeleton

boundary value problems for second order differential equations of sobolev type abstract in this paper we provide necessary and sufficient conditions for the existence and uniqueness of solutions of second order differential equations of sobolev type satisfying some boundary conditions we also give sufficient conditions so that the picard and approximate picard method converge to the unique solution of these boundary value problems

on three point boundary value problems associated with third order differential equations introduction in this paper we shall be concerned with the existence and uniqueness of solutions to three point boundary value problems associated with the differential equation y f x y y s y 1 1 where f x y z w is assumed to be continuous on a subset of r4 initial value problems associated with 1 1 exist and are unique in the interval x1 x a monotonicity restriction on f x y z w ensures that the following boundary value problems y j x y y y y xj y y xj y y x m i 1 2 12i y j x y y y y x y y x m2 2 2 9 y x y i 421 le3i

existence and uniqueness of solutions for nth order nonlinear two point boundary value problems in this paper we present some general results of existence and uniqueness of solutions for nth order nonlinear two point boundary value problems by using shooting method together with maximum principle and kneser hukahara continuum theorem as applications we give certain concrete sufficient conditions for the existence and uniqueness of solutions of nonlinear two point boundary value problems of nth order lipschitz equations

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

quasilinearization and approximate quasilinearization for multipoint boundary value problems quasilinearization technique has been applied to a general nonlinear lidstone boundary value problem for the construction of a sequence of its approximate solutions xn t sufficient conditions

effective computation of the multivariable alexander polinomial of lorenz links given two different representations of a lorenz link we compare how they affect the computation of the multivariable alexander polynomial we also compare the alexander polynomial with the trip number and genus our experimental results lead us to conjecture that for lorenz knots the alexander polynomial is an equivalent invariant to the pair trip number genus finally we give a counterexample in the case of lorenz links

topological invariants and renormalization of lorenz maps we prove that the invariants of the topological semiconjugation of lorenz maps with transformations remains constant on the renormalization archipelagoes and analyze how the dynamics on the archipelagoes depends on its structure

existence of solutions of right focal point boundary value problems for ordinary differential equations y f x y y y 1 1 with respect to l two conditions which we will assume are a f x y 7 yz y is continuous on a b x r b solutions of initial value problems for 1 are unique motivated by the idea of right disfocality of a linear nth order differential operator given by muldowney 11 we shall be concerned with uniqueness of solutions of 1 which satisfy boundary conditions of the form y l x yi 1 i n where x1 x q a x for related results in the linear case where x1 x x x see for example nehari 2 peterson 3 and elias 4 5 1 to be more definite we define what is meant by a right m 1 m focal point boundary value problem for 1 on an interval i

analytical and numerical solutions to two dimensional moving interface problems with applications to the solidification of killed steel ingots this paper is concerned with the development of methods for investigating moving interface problems that involve more than one space variable the work was motivated by problems arising from the british steel corporation scunthorpe concerning the solidification of killed steel ingots first we investigate certain two dimensional analytical solutions which simulate particular aspects of ingot solidification these relate to the inward solidification of a liquid half space either when the wall temperature varies with position along the wall or when newton cooling takes place at the wall with the local heat transfer coefficient a function of wall position other approximate analytical approaches with use of the heat balance integral method and formulation in terms of an integro differential equation are discussed briefly and their limited application to two dimensional problems noted a computer procedure is then developed for solving these half space problems and this yields results in exact agreement with the analytical solutions in the work special attention is given to obtaining reliable information for small stefan number beta l c p t f t 0 since this relates to values found in the steel making process in the major part of the paper a two dimensional mathematical model of ingot solidification is developed numerical solutions are given for an ingot when the mould surface varies in geometry and in composition good agreement is obtained with radio isotope tracer tests performed at the british steel corporation scunthorpe

a subdivision approach to the construction of approximate solutions of boundary value problems with deviating arguments abstract using the ideas employed in the construction of subdivision algorithms we offer here a high accuracy algorithm to compute numerical solutions for two point boundary value problems of differential equations with deviating arguments numerical examples are included to demonstrate the fast convergence and high accuracy of the algorithm this paper is a further development to our previous works for solving various types of boundary value problems

finite difference methods for boundary value problems of differential equations with deviating arguments abstract we propose a convergent finite difference method to construct an approximate solution of the boundary value problems with deviating arguments the method developed takes into account the continuity limitations of the solutions of these problems to demonstrate the effectiveness of the proposed method numerical evidence is also included

on the right focal point boundary value problems for integro differential equations abstract for the nth order nonlinear integro differential equations subject to right focal point boundary conditions we provide necessary and sufficient conditions for the existence uniqueness and convergence of an approximate iterative method

numerical methods for unilateral problems abstract the theory of variational inequalities besides being elegant and synthetic also provides a unified general framework for applying the numerical methods for solving many unrelated free boundary value problems in this paper we describe numerical experience on the use of variational inequalities and pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle in the case of a known obstacle these problems can be alternatively formulated as nonlinear boundary value problems without constraints for which the technique of pade approximants can be successfully employed the variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution

sinc galerkin method for solving nonlinear boundary value problems the sinc galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second fourth and sixth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on four nonlinear problems the results demonstrate the reliability and efficiency of the algorithm developed

uniqueness of solutions of right focal problems for third order differential equations on considere l unicite des solutions quand elles existent de certains problemes aux valeurs limites pour l equation differentielle d ordre 3 y f x y y y on suppose que f a b r 3 r est continue

numerical method for the solution of special nonlinear fourth order boundary value problems the sinc galerkin method is used to approximate solution of nonlinear problems this work deals with the sinc galerkin method for solving nonlinear fourth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on three nonlinear problems and a comparison with finite difference methods and fourth order multiderivative method is made it is shown that the sinc galerkin method yields better results

existence and uniqueness of solutions for third order nonlinear boundary value problems in this paper we present some general results of existence and uniqueness of solutions of nonlinear two point boundary value problems for third order nonlinear differential equations by using the shooting method as applications we give certain concrete sufficient conditions for the existence and uniqueness

boundary value problems occurring in plate deflection theory abstract the paper deals with several iterative methods for solving some boundary value problems occurring in plate deflection theory making it possible to avoid the lengthy problem preparation which is required to solve these problems by finite difference methods

the numerical solution of two generalizations of the neumann moving interface problem into two dimensions we present numerical solutions for the following stefan problems the half space z 0 is initially filled with liquid at its fusion temperature the boundary z 0 taken to be the x axis is maintained at a constant temperature less than the fusion temperature for x 0 the first problem considers the case of an insulated boundary and the second problem considers the case of the boundary maintained at the fusion temperature this gives rise to a solid liquid interface curved in the x z plane

method of chasing for multipoint boundary value problems the method of chasing developed by gel fand and lokutsiyevskii is completely formulated here for nth order ordinary linear differential equations subject to separated multipoint boundary conditions

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds

b spline collocation for solution of two point boundary value problems a numerical method based on b spline is developed to solve the general nonlinear two point boundary value problems up to order 6 the standard formulation of sextic spline for the solution of boundary value problems leads to non optimal approximations in order to derive higher orders of accuracy high order perturbations of the problem are generated and applied to construct the numerical algorithm the error analysis and convergence properties of the method are studied via green s function approach o h 6 global error estimates are obtained for numerical solution of these classes of problems numerical results are given to illustrate the efficiency of the proposed method results of numerical experiments verify the theoretical behavior of the orders of convergence

right focal point boundary value problems for ordinary differential equations and variational equations where x g x such problems are called right focal point boundary value problems in the last few years a number of papers have appeared dealing with such boundary value problems most notable in the case when 1 is linear are papers by elias 11 muldowney 7 8 and peterson 19 io and for nonlinear considerations the papers by henderson 3 4 jackson 5 and peterson 11 121 in those papers several analogues of known results for conjugate type boundary value problems are considered for eq l we will have need of the hypotheses