• # Sinc-Pack

• Referenced in 76 articles [sw13600]
• Handbook of Sinc numerical methods. With CD-ROM. This book deals with the approximation ... Sinc theory – 2. Sinc convolution-boundary integral equation methods for partial differential equations (PDEs...
• # ode23

• Referenced in 318 articles [sw06600]
• equations; low order method. [T,Y] = solver(odefun,tspan,y0) with tspan = [t0 tf] integrates ... system of differential equations y′ = f(t,y) from time t0 to tf with initial...
• # LIMbook

• Referenced in 59 articles [sw14520]
• Integral Methods for Conservative Problems. The book explains the numerical solution of differential equations within ... framework of geometric integration, a branch of numerical analysis that devises numerical methods able ... integral methods: the energy-conserving Runge-Kutta methods, also known as Hamiltonian boundary value methods ... numerical solution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energy-conserving...
• # INTLAB

• Referenced in 471 articles [sw04004]
• validating algorithms. It comprises of self-validating methods for dense linear systems (also inner inclusions ... nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations (simple and clusters ... fast) Gradients (to solve systems of nonlinear equations) Hessians (for global optimization) Taylor series ... sequential approach, slow for many variables) verified integration of (simple) univariate functions univariate and multivariate...
• # Taylor

• Referenced in 101 articles [sw10816]
• Taylor method for the numerical integration of initial value problems of ordinary differential equations (ODEs ... computer program that outputs a specific numerical integrator for a given set of ODEs ... authors discuss the performance of the resulting integrator in some examples, showing that ... integrations that require extended precision arithmetic. The main drawback is that the Taylor method...
• # EnKF

• Referenced in 408 articles [sw02066]
• EnKF is a sophisticated sequental data assimilation method. It applies an ensemble of model states ... model estimate, it applies ensemble integrations to predict the error statistics forward in time ... used in realistic applications with primitive equation models for the ocean and atmosphere. A recent...
• # BEMECH

• Referenced in 119 articles [sw10847]
• book describes applications of boundary element method (BEM) in solid mechanics, beginning with basic theory ... plasticity; b) the formulation of boundary integral equations for elasto-plasticity; c) the description ... algorithms for the implementation of boundary element method; d) the description of methods for evaluating...
• # CRACK

• Referenced in 58 articles [sw07754]
• computer program. A method to reduce the length of the equations for large bilinear algebraic ... systems is presented. The integrable polynomial vector evolution equations, quadratic Hamiltonians with...
• # MPSpack

• Referenced in 9 articles [sw14254]
• Eigenvalue Problems Using Particular Solutions and Integral Equations. MPSpack is a user-friendly and fully ... object-oriented MATLAB toolbox that implements the method of particular solutions, nonpolynomial ... method of fundamental solutions, and integral equation methods, for the efficient and highly accurate solution...
• # TABI

• Referenced in 32 articles [sw18194]
• linear Poisson-Boltzmann equation. The method employs a well-conditioned boundary integral formulation ... surface is triangulated and the integral equations are discretized by centroid collocation. The linear system...
• # SingularIntegralEquations

• Referenced in 10 articles [sw22771]
• fast and well-conditioned spectral method for singular integral equations. We develop a spectral method ... solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials ... reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing ... scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation...
• # REVE

• Referenced in 68 articles [sw28907]
• terminating term rewriting systems from sets of equations. Particular emphasis is placed on mechanization ... fully integrated into the algorithms. REVE uses an incremental termination method based on recursive decomposition ... from the presentation of the set of equations and which requires little knowledge of termination...
• # TIDES

• Referenced in 40 articles [sw06664]
• TIDES, a Taylor Series Integrator for Differential EquationS. We present a new free software called ... TIDES, based on the classical Taylor series method and using an optimized variable-stepsize variable...
• # Algorithm 838

• Referenced in 15 articles [sw04464]
• their derivatives of Airy’s differential equation, both on the real line ... axis. The computational methods are numerical integration of the differential equation and summation of asymptotic...
• # GELDA

• Referenced in 33 articles [sw00331]
• equations, see e.g. , ,. It is known that many of the standard integration ... methods for general DAEs require the system to have differentiation index not higher than...
• # MEBDF

• Referenced in 85 articles [sw00567]
• numerical integration of large sparse systems of stiff initial value ordinary differential equations and differential ... equations is described. The algorithm is constructed by embedding a standard sparse linear algebraic equation ... partial differential equations, particularly in two or more space dimensions, using the method of lines...