East Asian Journal on Applied Mathematics

The Landau-Lifshitz equation is a fundamental model in micromagnetics, whose nonlinear geometric structure arising from the pointwise unit-length constraint makes the construction of stable and accurate numerical schemes particularly challenging. In this work, we develop and analyze a class of extrapolated and linearized implicit-explicit Runge-Kutta (IMEX-RK) schemes within the generalized scala…

The Heston local-stochastic volatility (HLSV) model is used to investigate optimal consumption, life insurance, and investment strategies for a decision maker with habit formation and heterogeneous discounting. The decision maker can allocate wealth in a financial market consisting of risk-free and risky assets, where the price process of the risky asset follows the HLSV model. The habit formatio…

In recent years, physics-informed neural networks (PINNs) have emerged as an effective method for solving partial differential equations (PDEs). PINNs offer several advantages such as no limitation of dimensionality, low data requirements, and simple inverse problem solving. Introducing collocation points and PDE loss is the key to PINNs, while the distribution of collocation points significantly…

The rotating shallow water equations (RSWEs), incorporating the Coriolis force, induce the geostrophic equilibrium with a nonzero velocity field, which poses more challenges in designing well-balanced numerical schemes than solving the classical SWEs. To tackle this issue, we leverage the Coriolis force’s primitive function, specifically, the approach of apparent topography. Additionally, we intr…

The maximum bound principle (MBP) is an essential tool in understanding the key physical properties of parabolic partial differential equations. In this paper, we develop and analyze a novel, MBP-preserving, second-order nonuniform scheme for the Allen-Cahn model with general potential, namely, the integrating factor BDF2 scheme. Specifically, we employ the MBP-preserving iteration and an enhance…

An efficient modified Newton-PBGADI method for nonlinear systems with large sparse non-Hermitian positive definite Jacobian matrices is proposed. The method integrates a modified Newton framework that achieves $R-$order three convergence while requiring only a single inversion of the Jacobian matrix per iteration. The resulting linear subproblems are solved by a preconditioned block GADI method. …

We study a Riemannian gradient method for the $L_2-$Wasserstein least squares problem of Gaussian measures under the affine-invariant geometry. The variable of $L_2-$Wasserstein least squares problem lies in the set of positive definite matrices, which, equipped with the affine-invariant metric, forms a Hadamard manifold. The same set with usual Euclidean metric is also a Hadamard manifold, with …

This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter. Regarding the inverse problem, in addition to a basic indicator function based on the approximate solutions, a novel indicator function is developed to construct th…

Approximate solution of Fredholm integral equations with certain types of weakly singular algebraic kernels is obtained by the piecewise linear maximum entropy method. During implementation of the method, two-dimension numerical integration is reduced to one-dimension numerical integration, which allows to lower the computational cost. The results of numerical experiments are consistent with theo…

This paper explores integrable modified Korteweg-de Vries (mKdV) models using dual similarity transformations. Two representative examples involving distinct similarity transformations are presented, along with their corresponding reduced Ablowitz-Kaup-Newell–Segur matrix spectral problems. These examples illustrate how reduced matrix mKdV integrable models can be systematically generated through…

The Schrödinger bridge problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance and broad practical potential, with applications spanning a wide range of interdisciplinary fields. While theoretical aspects of the SBP are well-understood, prac…

In this paper, we introduce a new hybrid weighted essentially non-oscillatory (WENO) scheme grounded in trigonometric polynomials for the solution of Hamilton-Jacobi equations. This innovative approach utilizes trigonometric polynomial reconstruction as an alternative to the conventional algebraic polynomial reconstruction. Notably, the proposed scheme demonstrates reduced truncation errors in sm…

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing frequency variables and parameters inherited from the original model. To reduce the computational cost of the frequency-variable elliptic equations, we extend the …

This study investigates the natural convection flow of Williamson fluid between two concentric cylinders while affected by the radiation effect and magnetic field. The inner cylinder remains fixed while the outer cylinder rotates. Additionally, magnetic field is oriented radially, which influences the flow of the fluid. Applying a proper transformation, one transform the non-linear partial differ…

Heat transfer in composites is crucial in engineering, where imperfect layer contact induces thermal contact resistance (TCR), causing interfacial temperature jumps. We propose to solve this numerically using the optimized Schwarz method (OSM), which decouples the heterogeneous problem into homogeneous subproblems. This approach avoids ill-conditioned systems typical of monolithic methods under h…

This paper investigates the dynamics of the center of mass in three-dimensional arbitrary-angle rotating Bose-Einstein condensates (ARotBECs), which are governed by the Gross-Pitaevskii equation (GPE) with an arbitrary-angle angular momentum rotation term. The second-order ordinary differential equations (ODEs) which govern the motion of the center of mass of ARotBECs are analytically solved. Sub…

The paper proposes an energy-based adaptive sampling strategy to enhance the performance of the deep unfitted Nitsche method (DUNM) for elliptic interface problems. Instead of relying on fixed or random training points, the proposed refinement indicator dynamically concentrates samples in high-energy regions, including sharp coefficient jumps and interface singularities. This targeted allocation …

A variable-coefficient Sawada-Kotera system is investigated that models the nonlinear behaviors of waves in shallow water, ion-acoustic waves in plasma environments and fluid flow dynamics. The Painlevé integrability is tested by the WTC method with the simplified form of Krustal. The Hirota bilinear method is employed to derive the bilinear form. Consequently, we obtain a variety of analytic sol…

A discontinuous Galerkin (DG) method on Bakhvalov-type (B-type) meshes for singularly perturbed Volterra integro-differential equations (SPVIDEs) is proposed. We derive abstract error bounds of the DG method for the SPVIDEs in the $L^2$-norm. It is shown that the approximate solution generated by the DG method on B-type meshes has optimal convergence rate $k + 1$ in the $L^2$-norm, when using the…