7 Result(s)
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Article
Akitoshi Takayasu
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Article
Open AccessSaddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining...
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Open AccessComplex moment-based methods for differential eigenvalue problems
This paper considers computing partial eigenpairs of differential eigenvalue problems (DEPs) such that eigenvalues are in a certain region on the complex plane. Recently, based on a “solve-then-discretize” par...
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Open AccessCorrection to: Rigorous numerics for nonlinear heat equations in the complex plane of time
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Open AccessRigorous numerics for nonlinear heat equations in the complex plane of time
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explici...
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Numerical validation of blow-up solutions with quasi-homogeneous compactifications
We provide a numerical validation method of blow-up solutions for finite dimensional vector fields admitting asymptotic quasi-homogeneity at infinity. Our methodology is based on quasi-homogeneous compactifica...
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Rigorous numerical computations for 1D advection equations with variable coefficients
This paper provides a methodology of verified computing for solutions to 1D advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic...
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Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimatio...
