Authors:Achamyelesh A. Aligaz, Justin M. W. Munganga Pages: 1 - 20 Abstract: We present and analyze a mathematical model of the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) in the presence of antibiotic treatment with limited medical supply. We use a saturated treatment function to model the effect of delayed treatment. We prove that there exist one disease free equilibrium and at most two endemic equilibrium solutions. A backward bifurcation occurs for small values of delay constant such that two endemic equilibriums exist if Rt ∈ (R∗t,1); where, Rt is the treatment reproduction number and R∗t is a threshold such that the disease dies out if and persists in the population if Rt > R∗t. However, when a backward bifurcation occurs, a disease free system may easily be shifted to an epidemic. The bifurcation turns forward when the delay constant increases; thus, the disease free equilibrium becomes globally asymptotically stable if Rt < 1, and there exist unique and globally asymptotically stable endemic equilibrium if Rt > 1. However, the amount of maximal medical resource required to control the disease increases as the value of the delay constant increases. Thus, antibiotic treatment with limited medical supply setting would not successfully control CBPP unless we avoid any delayed treatment, improve the efficacy and availability of medical resources or it is given along with vaccination. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.11795 Issue No:Vol. 26, No. 1 (2021)

Authors:Antanas Laurinčikas, Darius Šiaučiūnas, Gediminas Vadeikis Pages: 21 - 33 Abstract: In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R. In the paper, the Mishou theorem is generalized for the set of above shifts having a weighted positive lower density. Also, the case of a positive density is considered. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12445 Issue No:Vol. 26, No. 1 (2021)

Authors:Elmira A. Bakirova, Anar T. Assanova, Zhazira M. Kadirbayeva Pages: 34 - 54 Abstract: The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.11977 Issue No:Vol. 26, No. 1 (2021)

Authors:Kristina Kaulakytė, Neringa Klovienė Pages: 55 - 71 Abstract: The nonhomogeneous boundary value problem for the stationary NavierStokes equations in 2D symmetric multiply connected domain with a cusp point on the boundary is studied. It is assumed that there is a source or sink in the cusp point. A symmetric solenoidal extension of the boundary value satisfying the LerayHopf inequality is constructed. Using this extension, the nonhomogeneous boundary value problem is reduced to homogeneous one and the existence of at least one weak symmetric solution is proved. No restrictions are assumed on the size of fluxes of the boundary value. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12173 Issue No:Vol. 26, No. 1 (2021)

Authors:Roberto Garra, Zivorad Tomovski Pages: 72 - 81 Abstract: In this paper we obtain some new explicit results for nonlinear equations involving Laguerre derivatives in space and/or in time. In particular, by using the invariant subspace method, we have many interesting cases admitting exact solutions in terms of Laguerre functions. Nonlinear diffusive-type and telegraph-type equations are considered and also the space and time-fractional counterpart are analyzed, involving Caputo or Prabhakar-type derivatives. The main aim of this paper is to point out that it is possible to construct many new interesting examples of nonlinear diffusive equations with variable coefficients admitting exact solutions in terms of Laguerre and Mittag-Leffler functions. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.11270 Issue No:Vol. 26, No. 1 (2021)

Authors:Aidas Balčiūnas, Violeta Franckevič, Virginija Garbaliauskienė, Renata Macaitienė, Audronė Rimkevičienė Pages: 82 - 93 Abstract: It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ ∈ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12447 Issue No:Vol. 26, No. 1 (2021)

Authors:Bahar Karaman Pages: 94 - 115 Abstract: This research describes an efficient numerical method based on Wendland’s compactly supported functions to simulate the time-space fractional coupled nonlinear Schrödinger (TSFCNLS) equations. Here, the time and space fractional derivatives are considered in terms of Caputo and Conformable derivatives, respectively. The present numerical discussion is based on the following ways: we first approximate the Caputo fractional derivative of the proposed equation by a scheme order O(∆t2−α), 0 < α < 1 and then the Crank-Nicolson scheme is employed in the mentioned equation to discretize the equations. Second, applying a linear difference scheme to avoid solving nonlinear systems. In this way, we have a linear, suitable calculation scheme. Then, the conformable fractional derivatives of the Wendland’s compactly supported functions are established for the scheme. The stability analysis of the suggested scheme is also examined in a similar way to the classic Von-Neumann technique for the governing equations. The efficiency and accuracy of the present method are verified by solving two examples. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12262 Issue No:Vol. 26, No. 1 (2021)

Authors:Saeid Abbasbandy, Hussein Sahihi, Tofigh Allahviranloo Pages: 116 - 134 Abstract: In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12057 Issue No:Vol. 26, No. 1 (2021)

Authors:Mansur I. Ismailov Pages: 135 - 146 Abstract: We consider the Mullins’ equation of a single surface grooving when the surface diffusion is not considered as very slow. This problem can be formed by a surface grooving of profiles in a finite space region. The finiteness of the space region allows to apply the Fourier series analysis for one groove and also to consider the Mullins coefficient as well as slope of the groove root to be time-dependent. We also solve the inverse problem of finding time-dependent Mullins coefficient from total mass measurement. For both of these problems, the grooving side boundary conditions are identical to those of Mullins, and the opposite boundary is accompanied by a zero position and zero curvature which both together arrive at self adjoint boundary conditions. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12432 Issue No:Vol. 26, No. 1 (2021)

Authors:Mart Ratas, Andrus Salupere, Jüri Majak Pages: 147 - 169 Abstract: The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon equation are used as model equations. Adaptive as well as nonadaptive nonuniform grids are developed and used to solve the model equations numerically. The numerical results are compared to the known analytical solutions as well as to the numerical solutions obtained by application of the HOHWM on a uniform grid. The proposed methods of using nonuniform grid are shown to significantly increase the accuracy of the HOHWM at the same number of grid points. PubDate: 2021-01-18 DOI: 10.3846/mma.2021.12920 Issue No:Vol. 26, No. 1 (2021)