multiple solutions for 2mth order sturm liouville boundary value problems growth conditions are imposed on f such that the following boundary value problem 1 my 2m f t y i 1y 2i 0 i 1y 2i 1 0 i 1y 2i 1 i 1y 2i 1 1 0 0 i m 1 has an arbitrary number of positive solutions

higher order schemes with cip method and adaptive soroban grid towards mesh free scheme a new class of body fitted grid system that can keep the third order accuracy in time and space is proposed with the help of the cip constrained interpolation profile cubic interpolated propagation method the grid system consists of the straight lines and grid points moving along these lines like abacus soroban in japanese the length of each line and the number of grid points in each line can be different the cip scheme is suitable to this mesh system and the calculation of large cfl 10 at locally refined mesh is easily performed mesh generation and searching of upstream departure point are very simple and almost mesh free treatment is possible adaptive grid movement and local mesh refinement are demonstrated

a comparative study of characteristic based algorithms for the maxwell equations characteristic based finite difference and finite volume schemes have been developed for solving the three dimensional maxwell equations in the time domain a detailed eigenvector analysis for the maxwell equations in a general curvilinear coordinate has also been completed to provide a basic framework for future finite difference schemes although the basic concepts of the two algorithms are identical the detailed formulations are vastly different for achieving split flux vectors according to the sign of the eigenvalues a comparative study of these algorithms applied to an oscillating electric dipole is carried out to assess their relative merit for further development in spherical coordinates second order windward numerical simulations of the radiating phenomenon are closely comparable in terms of accuracy and efficiency these methods also demonstrate an ability to suppress reflected waves from the truncated boundary by a simple compatibility condition

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

consideration of treatment of the boundary between different media in electromagnetic field analysis using the constrained interpolation profile method the treatment of a boundary between different media to simulate an electromagnetic em field is examined using the constrained interpolation profile cip method consideration of the way of handling spatial derivatives of fields is very important for cip em field analysis we demonstrate a method of handling this boundary and report results of cip em field analysis using the present approach

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

a fractional step method for solving 3d time domain maxwell equations abstract stable and efficient implicit and explicit fractional step methods for solving three dimensional time dependent maxwell equations have been successfully developed these numerical procedures are characteristic based schemes with the intrinsically accurate no reflection wave condition on the boundaries of truncated computational domain excellent simulations tot electromagnetic phenomena have been achieved for a three dimensional wave guide and an oscillating electric dipole

stability analysis of a prey predator model with holling type iii response function incorporating a prey refuge in this paper we consider a prey predator model with holling type iii response function incorporating a prey refuge the purpose of the work is to offer mathematical analysis of the model and to discuss some significant qualitative results that are expected to arise from the interplay of biological forces some numerical simulations are carried out

existence of multiple symmetric positive solutions of higher order lidstone problems this paper gives the sufficient conditions of the existence of at least three symmetric positive solutions for one type of higher order autonomous lidstone problem by applying the five functionals fixed point theorem the analogous result for higher order nonautonomous singular lidstone problem is also proved here

a discrete time version for models of population dynamics in the presence of an infection we present a set of difference equations which represents the discrete counterpart of a large class of continuous model concerning the dynamics of an infection in an organism or in a host population the limiting behavior of the discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived

positive solutions for higher order lidstone boundary value problems a new approach via sperner s lemma abstract consider the higher order nonlinear scalar differential equation where associated to the lidstone boundary conditions existence of a solution of boundary value problems bvp 1 2 such that are given under superlinear or sublinear growth in f similarly existence for the bvp 1 3 under the same assumptions is proved such that we further prove analogous results for the case when i e derivatives of the obtaining solution satisfy inverse inequalities the approach is based on an analysis of the corresponding vector field on the face plane and the well known from combinatorial analysis knaster kuratowski mazurkiewicz s principle or as it is known sperner s lemma

a finite volume method for the maxwell equations in the time domain a finite volume scheme for the maxwell equations is proposed using collocated nonorthogonal curvilinear grid arrangements with the advantage that all components of the electric and magnetic field are stored at the same computational location and time it is based on construction principles of high resolution schemes for hyperbolic conservation laws and takes into account the local wave propagation the implementation of boundary conditions based on the characteristic theory is described a new divergence correction technique is proposed to preserve locally the charge conservation this is important if the maxwell solver is used within an electromagnetic particle in cell pic code the accuracy and efficiency of this finite volume framework is demonstrated with problems of electromagnetic wave propagation and of the self consistent motion of charged particles

analysis of an electromagnetic field created by line current using constrained interpolation profile method development of accurate schemes is a technical issue related to calculation of electromagnetic fields this study uses constrained interpolation profile cip method to analyze electromagnetic fields created by line current this is a novel method proposed by yabe comparison of results obtained using finite difference time domain fdtd analysis and cip analysis indicates that cip analysis provides higher accuracy using identical discretization in addition given the same level of accuracy cip analysis requires less memory and less calculation time

time domain electromagnetic scattering simulations on multicomputers a series of bistatic radar cross sections of a perfectly conducting sphere over a frequency range were processed on one shared and three distributed memory computers a comparative study was conducted for both the total field and the scattered field formulations the accuracy criteria for the grid point density per wavelength and the placement of the truncated far field boundary were also established for the present characteristic based finite volume scheme the numerical accuracy of all simulations has been validated with theoretical results

chaotic dynamics of a discrete predator prey system with prey refuge prey predator system with prey refuge for the case of non overlapping generations is considered here for our present study foraging efficiency of predator largely varies with the escaping ability of the prey from the predator for this reason system experiences interesting and complex dynamical features with varying the strength of prey refuge including both population extinction predator extinction stable coexistence multiple invariant closed orbit in different chaotic regions onset of chaos suddenly and sudden disappearance of the chaotic dynamics in particular we observe that when the prey is in stable oscillatory or even chaotic status then the predator can tend to extinction also system experiences hopf bifurcation and flip bifurcations numerical computation is also performed to validate and visualize different theoretical results the computations of lyapunov exponent fractal dimension of the map recurrence plot and power spectral density confirm the chaotic dynamical behaviors the analysis and results in this paper are interesting both in mathematics and biology

cubic interpolated pseudo particle method cip for solving hyperbolic type equations abstract a new cubic polynomial interpolation method where the gradient of the quantity is a free parameter is proposed for solving hyperbolic type equations various choices of the gradient are investigated and a stable and less diffusive scheme is made possible without the clipping or the flux correction procedure

further investigations into the stability and bifurcation of a discrete predator prey model abstract in this paper we revisit a discrete predator prey model with a non monotonic functional response originally presented in hu teng and zhang 2011 6 first by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points e 3 and e 4 obtained in this article we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria here we present a very useful lemma which is a corrected version of a known result and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system we then study the stability and bifurcation for the equilibrium point e 1 of this system which has not been considered in any known literature unlike known results that present a large number of mathematical formulae that are not easily verified we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation which are explicitly expressed by the coefficient of the system the center manifold theory and project method are the main tools in the analysis of bifurcations the theoretical results obtained are further illustrated by numerical simulations

bifurcation analysis and chaos in a discrete reduced lorenz system in this paper the discrete reduced lorenz system is considered the dynamical behavior of the system is investigated the existence and stability of the fixed points of this system are derived the conditions for existence of a pitchfork bifurcation flip bifurcation and neimark sacker bifurcation are derived by using the center manifold theorem and bifurcation theory the complex dynamics bifurcations and chaos are displayed by numerical simulations

solutions of two point boundary value problems for even order differential equations abstract the existence of solutions of the two point boundary value problems consisting of the even order differential equations x 2 n t f t x t x t x 2 n 2 t r t 0 t 1 and the boundary value conditions i x 2 i 0 i x 2 i 1 0 0 i x 2 i 1 i x 2 i 1 1 0 i 0 1 n 1 is studied sufficient conditions for the existence of at least one solution of above bvps are established it is interesting that the nonlinearity f in the equation depends on all lower derivatives especially odd order derivatives and the growth conditions imposed on f are allowed to be super linear the degrees of phases variables are allowed to be greater than 1 if it is a polynomial the results are different from known ones since we do not apply the green s functions of the corresponding problem and the method to obtain a priori bounds of solutions is different from known ones examples that cannot be solved by known results are given to illustrate our theorems