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Quaternionic analysis initiated new solution methods for boundary value problems in several research areas of mathematical physics, in particular in planar fluids, quantum field theory, electromagnetic wave equations etc.
Several algorithms based on shooting methods for boundary value problems are used in this task, and some appropriate ways of tackling the simple initial value problem of simulation are also employed.
Since the proof of the main theorem (Theorem 4.1) in this paper is independent of the expression form of and only dependent on its continuity and nonnegativity, there are similar conclusions by analogous methods for boundary value problems (1.5) subject to other boundary value conditions, respectively, the following.
In view of their C∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc.
One reason for this is that so-called fast methods for boundary integral operators usually deal with discrete functions, cf. [43].
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For the topology optimization of each ply, we lean on the level set method for the description of the interfaces and the Hadamard method for boundary variations by means of the computation of the shape gradient.
In this paper the recently introduced backstepping method for boundary control of linear partial differential equations (PDEs) is extended to plants with non-constant diffusivity/thermal conductivity and time-varying coefficients.
R package bvpSolve implements the method for boundary value problem [ 15].
It is very feasible for numerical methods, especially for boundary element method (BEM) which can directly present the unknown boundary values.
Multiple methods exist for boundary delineation such as two-dimensional wombling, constrained classification techniques and discontinuity detection.
The relation between the boundary- and finite-element method for boundary-value problems governed by linear, homogeneous, and elliptic differential equations is discussed.
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