Browsing by Author "Yunus, AAM"
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Publication Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions(Hindawi Ltd, 2012) ;Yunus, AAM ;Murid, AHMNasser, MMSWe present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels. - Some of the metrics are blocked by yourconsent settings
Publication Conformal Mapping of Unbounded Multiply Connected Regions onto Logarithmic Spiral Slit with Infinite Straight Slit(Amer Inst Physics, 2017) ;Yunus, AAMMurid, AHMThis paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for conformal mapping of unbounded multiply connected regions. The canonical region is the entire complex plane bounded by an infinite straight slit on the line Im omega = 0 and finite logarithmic spiral slits. Some linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on a multiply connected region. These integral equations are uniquely solvable. The kernel involved in these integral equations is the adjoint generalized Neumann kernel. - Some of the metrics are blocked by yourconsent settings
Publication Cubes of Finite Vertices Fuzzy Topographic Topological Mapping and k-Fibonacci Sequence(Amer Inst Physics, 2018) ;Yunus, AAMAhmad, TFuzzy Topographic Topological Mapping (FTTM) is a model for solving neuromagnetic inverse problem. FTTM consists of four components and connected by three algorithms. FTTM version 1 and FTTM version 2 were designed to present 3D view of an unbounded single current and bounded multicurrent sources, respectively. In 2008, Suhana introduced some definitions on sequence of FTTM. One of the features produced from the sequences of FTTM is Cube of FTTM. A cube of FTTM is a combination of two or more FTTM in FTTM. In this paper, cube of finite vertices of FTTM, namely FKn are discussed. Consequently, some theorems are proven in order to describe patterns for sequence of cubes for FKn based on this k-Fibonacci sequence. Interestingly, the cube of FKn appears to be an example of generalized Fibonacci sequence, namely the k-Fibonacci sequence. - Some of the metrics are blocked by yourconsent settings
Publication Effective Quadrature Formula in Solving Linear Integro-Differential Equations of Order Two(AMER INST PHYSICS, 2017) ;Eshkuvatov, ZK ;Kammuji, M ;Long, NMANYunus, AAMIn this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed. - Some of the metrics are blocked by yourconsent settings
Publication Matrix Form of Legendre Polynomials for Solving Linear Integro-Differential Equations of High Order(Amer Inst Physics, 2017) ;Kammuji, M ;Eshkvatov, ZKYunus, AAMThis paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transtbnn FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods - Some of the metrics are blocked by yourconsent settings
Publication Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions(Royal Soc, 2014) ;Yunus, AAM ;Murid, AHMNasser, MMSThis paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used for computing the mapping function and its inverse for interior points. This method also works for regions with piecewise smooth boundaries. Three examples are given to illustrate the effectiveness of the proposed method. - Some of the metrics are blocked by yourconsent settings
Publication Numerical Conformal Mapping onto the Entire Complex Plane Bounded with Finite Straight Slit and Logarithmic Spiral Slits(IOP Publishing Ltd, 2019) ;Yunus, AAM ;Yunus, ANasser, MMSThis paper presents a fast boundary integral equation method with for computing conformal mappings of multiply connected regions. We consider the canonical region consists of the entire complex plane bounded by a finite straight slit on the line Im ( )omega = 0 and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method. - Some of the metrics are blocked by yourconsent settings
Publication Numerical Conformal Mapping onto the Exterior Unit Disk with a Straight Slit and Logarithmic Spiral Slits(IOP Publishing Ltd, 2019) ;Murid, AHM ;Yunus, AAMNasser, MMSThis paper presents a fast boundary integral equation method for numerical conformal mapping of unbounded multiply connected regions onto a disk with an infinite straight slit and finite logarithmic spiral slits. Some numerical examples are given to show the effectiveness of the proposed method. - Some of the metrics are blocked by yourconsent settings
Publication Numerical Evaluation of Conformal Mapping and its Inverse for Unbounded Multiply Connected Regions(Malaysian Mathematical Sciences Soc, 2014) ;Yunus, AAM ;Murid, AHMNasser, MMSA boundary integral equation method for numerical evaluation of the conformal mapping and its inverse from unbounded multiply connected regions onto five canonical slit regions is presented in this paper. This method is based on a uniquely solvable boundary integral equation with the adjoint generalized Neumann kernel. This method is accurate and reliable. Some numerical examples are presented to illustrate the effectiveness of this method. - Some of the metrics are blocked by yourconsent settings
Publication Radial Slits Maps of Unbounded Multiply Connected Regions(Amer Inst Physics, 2013) ;Yunus, AAM ;Murid, AHMNasser, MMSThis paper presents a boundary integral equation method for conformal mapping of an unbounded multiply connected region onto a radial slits region. Two linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. These integral equations are uniquely solvable. The kernels involved in these integral equations are the adjoint generalized Neumann kernels. Two numerical examples are presented to show the effectiveness of the proposed method.