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In this paper, we are interested in finding a numerical solution of a linear BVP for a Fredholm IDE with a degenerate kernel subjected to impulsive actions. By Dzumabaev's parametrization method the original problem is reduced to a multipoint BVP for the system of Fredholm IDEs with additional parameters. For fixed parameters, the special Cauchy problem for the system of FIDEs on subintervals is obtained and by using a solution to this problem, a system of algebraic equations in parameters is constructed. An algorithm for solving the BVP and its computational implementation is developed. In the algorithm, Cauchy problems for ODEs and the calculation of definite integrals are the main auxiliary problems. By using various numerical methods for solving these auxiliary problems, the proposed algorithm can be implemented in different ways. The program codes were written to solve the problem and all calculations are performed on the Matlab 2018 software platform. [ABSTRACT FROM AUTHOR]

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a highorder compact PRADI likemethod. Both of themhave the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms. [ABSTRACT FROM AUTHOR]

The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct a group of Saul'yev type asymmetric difference formulas for the dispersive equation. Based on these formulas we derive a new alternating 6-point group algorithm to solve dispersive equations with periodic boundary conditions. The algorithm has a high-order accuracy in space and an unconditional stability. The theoretical results are conformed to the numerical simulation. A comparison of this algorithm with the previous Alternating Group Explicit method is presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiresolution adaptive mesh refinement algorithm for solving initial-boundary value problems (IBVP) for evolution PDEs. The proposed algorithm dynamically adapts the grid to any existing or emerging irregularities in the solution, by refining the grid only at those places where the solution exhibits sharp features. The main advantage of the proposed grid adaptation method is that it results in a grid with a fewer number of nodes when compared to adaptive grids generated by existing multiresolution-based mesh refinement techniques. Several examples show the robustness and stability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper,we present a new algorithm to solve a kind of singular boundary-value problems of higher even-order based on the theory of numerical analysis in the reproducing kernel space . Singular boundary-value problem of sixth-order has been discussed for the problem in the case of . The numerical results are compared with both the exact solution and its -order derived functions in the example. It is demonstrated that our method is of high precision and significance. [Copyright &y& Elsevier]

Abstract  In this paper we present an efficient numerical algorithm for solving linear and nonlinear boundary value problems with two-point boundary conditions of tenth-order. The differential transform method is applied to construct the numerical solutions. The proposed algorithm avoids the complexity provided by other numerical approaches. Several illustrative examples are given to demonstrate the effectiveness of the present algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries. The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary in under mean curvature flow. For n =3 the problem has been approached in D.L. Chopp, 1993 and L.-T. Cheng [D.L. Chopp, Computing minimal surfaces via level set curvature flow, J. Comput. Phys. 106(1) (1993) 77–91 and L.-T. Cheng, The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using the level set method, but with a more complicated boundary conditions. The method we present can be generalized straightforward to arbitrary dimension, and the framework in which it is presented is dimension independent. Examples are shown for n =2, 3, 4. [Copyright &y& Elsevier]

In this paper, we investigate the method of the numerical solution of boundary value problems in inhomogeneous domains composed of homogeneous multidimensional parallelepipeds. The method is the symbiosis of high-order difference schemes in homogeneous subdomains and multipoint one-dimensional boundary conditions at interfaces. Due to splitting, the boundary value problem reduces to systems of linear algebraic equations with matrices different from a tridiagonal matrix by the availability of separate 'long' rows with more than three nonzero elements. Two algorithms are investigated to solve these systems. The first algorithm is based on the immediate transformation of the system of equations to a tridiagonal form. The second one is a generalization of the known sweep parallelizing method. [ABSTRACT FROM AUTHOR]