Search · four archives
Search · four archives
25 papers · ranked by Valyu relevance
Lie-jun Xie, Cai-lian Zhou, Song Xu
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the…
Randhir Singh, Jitendra Kumar, Gnaneshwar Nelakanti
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the…
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, Ihsanul Haq
'Ihsanul Haq'] We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error…
Randhir Singh
In this work, we apply Adomian decomposition method for solving nonlinear derivativedependent doubly singular boundary value problems: (py′ ) ′ = qf(x, y, y′ ). This method is based on the modification of ADM and new two-fold integral operator. The approximate solution is obtained in the form of series with easily…
Waseem Waseem, Muhammad Sulaiman, Poom Kumam, Muhammad Shoaib + 3 more
'Muhammad Asif Zahoor Raja' 'Saeed Islam' 'Hector Vazquez-Leal'] In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown…
Andrei D. Polyanin, Inna K. Shingareva
(ii) in hypersingular boundary-value problems, the position of the boundary layer is determined by the values of the unknown function at the boundaries (in standard problems with boundary layers, the position of the boundary layer is determined by coefficients of the given equation, and the values of the unknown…
Markus Rosenkranz, J. Liu, Alexander Maletzky, Bruno Buchberger
We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic approach, with (partial) implementation in the Theorema software system (which is based…
Bandyopadhyay, Shalmali, Kunkel, Curtis J
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a positive solution and obtain the desired solution by using a sequence of solutions…
Süleyman Cengizci, Mehmet Tarık Atay, Aytekin Eryılmaz
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid…
J.L. Gracia, Eugene O’Riordan
Numerical approximations to the solutions of three different problem classes of singularly perturbed parabolic reaction-diffusion problems, each with a discontinuity in the boundary-initial data, are generated. For each problem class, an analytical function associated with the discontinuity in the data, is identified.…
Han Xu, Yinlai Jin
We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Pingrun Li
In this article, we study some classes of singular integral equations of convolution type with Cauchy kernels in the class of exponentially increasing functions. Such equations are transformed into Riemann boundary value problems on either a straight line or two parallel straight lines by Fourier transformation. We…
Ababi Hailu Ejere, Gemechis File Duressa, Mesfin Mekuria Woldaregay, Tekle Gemechu Dinka
'Tekle Gemechu Dinka'] In this study, a parameter-uniform numerical scheme is built and analyzed to treat a singularly perturbed parabolic differential equation involving large spatial delay. The solution of the considered problem has two strong boundary layers due to the effect of the perturbation parameter, and the…
Nikos I. Kavallaris, Farrukh Javed
We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction–diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Pilar Herreros
We also use this functional to construct nonlinearities f such that this problem has at least two bound state solutions that change sign j times, for j = 1, . . . , k − 1. And another f such that this problem has a unique ground state solution, and at least two bound state solutions that change sign one time.
I. V. Boykov
| Abstract | 4 | | --- | --- | | Preface | 4 | | Introduction | 10 | | 1. Classes of Functions | 10 | | 2. Designations and Auxiliary Statements | 12 | | 2.1. Designations of Optimal Algorithms | 12 | | 2.2. Elements of Functional Analysis | 14 | | 2.3. Elements of Approximation Theory | 19 | | 2.4. Inverse Theorems |…
Mahdiar Sadeghi, M. Ali Al-Radhawi, Michael Margaliot, Eduardo Sontag
The control input λ_0_(t) appears linearly in the the Hamiltonian (11), and also p_2_(t) ≡ p_2_(0) which follows from (13) since . Hence, we can define the switching function as: We have the following lemma: Lemma 3. Let be an optimal trajectory, then if φ(t) ≠ 0, then: i.e, λ_0_(t) is a bang-bang control when the…
Emine Atıcı Endes, Neslihan Nesliye Pelen
Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the specific conditions that convert stable plaques into unstable ones remain unclear. To provide insight into the conditions for this…
David Thompson, Johan Gielis
Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Tracey Oellerich, Maria Emelianenko, Lance Liotta, Robyn P. Araujo
This work is focused on Ordinary Differential Equations(ODE)-based models of biochemical systems that possess a singular Jacobian manifesting in non-hyperbolic equilibria. We show that there are several classes of systems that exhibit this behavior: a)systems with monomial-type interaction terms and b)systems with…
Wolfgang Quapp, Josep Maria Bofill
We contradict diverse mathematical claims of a paper by Casey O. Barkan and Robijn F. Bruinsma in PNAS 2024, 121, No. 6, e2315866121, former BioRxiv preprint from Sept.12,2023. It deals with the physical mechanisms of protein-ligand catch bonding for the family of selectin proteins. Selectins exhibit slip, catch–slip…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…