Lawrence Fred Shampine
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Why Is Lawrence Fred Shampine Influential?
(Suggest an Edit or Addition)Lawrence Fred Shampine's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- The MATLAB ODE Suite (1997) (3220)
- Computer solution of ordinary differential equations : the initial value problem (1975) (1325)
- Solving ODEs with MATLAB (2003) (731)
- Numerical Solution of Ordinary Differential Equations (1995) (588)
- A BVP solver based on residual control and the Maltab PSE (2001) (546)
- Solving DDEs in MATLAB (2001) (540)
- A 3(2) pair of Runge - Kutta formulas (1989) (537)
- Vectorized adaptive quadrature in MATLAB (2008) (438)
- Solving Index-1 DAEs in MATLAB and Simulink (1999) (415)
- Computer Solution of Ordinary Differential Equations. (1981) (365)
- Solving Boundary Value Problems for Ordinary Differential Equations in M atlab with bvp 4 c (357)
- A User’s View of Solving Stiff Ordinary Differential Equations (1979) (309)
- A collocation method for boundary value problems (1972) (307)
- Solving Nonstiff Ordinary Differential Equations—The State of the Art (1976) (242)
- Analysis and implementation of TR-BDF2 (1996) (235)
- Block Implicit One-Step Methods* (1969) (217)
- A BVP Solver that Controls Residual and Error 1 (2008) (196)
- RKC: an explicit solver for parabolic PDEs (1998) (195)
- Numerical Methods for Singular Boundary Value Problems (1975) (185)
- Interpolation for Runge–Kutta Methods (1985) (124)
- Automatic Solution of the Sturm-Liouville Problem (1978) (120)
- Solving Hyperbolic PDEs in MATLAB (2005) (114)
- Solving ODEs and DDEs with residual control (2005) (103)
- DEPAC - design of a user oriented package of ODE solvers (1980) (103)
- Implementation of Implicit Formulas for the Solution of ODEs (1980) (102)
- Numerical computing: An introduction (1973) (98)
- Reliable solution of special event location problems for ODEs (1991) (98)
- A-stable block implicit one-step methods (1972) (93)
- Implementation of Rosenbrock Methods (1982) (90)
- An efficient Runge-Kutta (4,5) pair (1996) (90)
- Event location for ordinary differential equations (2000) (90)
- A User-Friendly Fortran BVP Solver (2006) (86)
- Fundamentals of Numerical Computing (1997) (81)
- Matlab program for quadrature in 2D (2008) (80)
- Error Estimation and Control for ODEs (2005) (80)
- Algorithm 876: Solving Fredholm Integral Equations of the Second Kind in Matlab (2008) (69)
- Global Error Estimates for Ordinary Differential Equations (1976) (68)
- Conservation laws and the numerical solution of ODEs, II (1999) (68)
- The art of writing a Runge-Kutta code. II. (1979) (65)
- Initial value problems for ODEs in problem solving environments (2000) (64)
- Applications of the Maximum Principle to Singular Perturbation Problems. (1973) (63)
- Solving Delay Differential Equations with dde 23 (2000) (63)
- Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods (1977) (62)
- A friendly Fortran DDE solver (2006) (61)
- Practical aspects of interpolation in Runge-Kutta codes (1987) (58)
- Automatic selection of the initial step size for an ODE solver (1987) (57)
- Numerical Solution of Delay Differential Equations (2009) (57)
- Solving 0 = F(t, y(t), y′(t)) in Matlab (2002) (54)
- Using AD to solve BVPs in MATLAB (2005) (52)
- The Art of Writing a Runge-Kutta Code, Part I (1977) (52)
- Evaluation of a Test Set for Stiff ODE Solvers (1981) (51)
- Two-step Lax-Friedrichs method (2005) (48)
- IRKC: an IMEX solver for stiff diffusion-reaction PDEs (2006) (48)
- Delay-differential-algebraic equations in control theory (2006) (46)
- Non-negative solutions of ODEs (2005) (45)
- Comparing Error Estimators for Runge-Kutta Methods (1971) (45)
- Singular boundary value problems for ODEs (2003) (44)
- Tolerance proportionality in ODE codes (1989) (41)
- RKSUITE: A Suite of Explicit Runge-Kutta Codes (1993) (39)
- Accurate numerical derivatives in MATLAB (2007) (37)
- Concentration-dependent diffusion. II. Singular problems (1973) (34)
- Type-insensitive ODE codes based on implicit A-stable formulas (1981) (31)
- Some Singular Concentration Dependent Diffusion Problems (1973) (31)
- Local extrapolation in the solution of ordinary differential equations (1972) (31)
- Implicitly defined output points for solutions of ODEs (1980) (31)
- Response of a String to an Accelerating Mass (1976) (29)
- Local error control in codes for ordinary differential equations (1977) (29)
- Error estimators for stiff differential equations (1984) (29)
- Stiffness and Non-Stiff Differential Equation Solvers (1975) (28)
- Initial value problems (2007) (28)
- ODE solvers and the method of lines (1994) (26)
- Dissipative approximations to neutral DDEs (2008) (25)
- Art of writing a Runge--Kutta code (1976) (24)
- Detecting stiffness with the Fehlberg (4, 5) formulas (1977) (23)
- A simple step size selection algorithm for ODE codes (1995) (21)
- Curve fitting by polynomials in one variable (1974) (21)
- Local error estimation by doubling (1985) (20)
- Error estimation and control for ODEs (2005) (20)
- The first and second boundary value problems for nonlinear second order differential equations (1966) (20)
- The step sizes used by one-step codes for ODEs☆ (1985) (19)
- Algorithm 504: GERK: Global Error Estimation For Ordinary Differential Equations [D] (1976) (19)
- Estimating conditioning of BVPs for ODEs (2004) (19)
- Limiting precision in differential equation solvers (1974) (19)
- Stability of the leapfrog/midpoint method (2009) (18)
- Fixed versus variable order Runge-Kutta (1986) (18)
- Stiff systems (2007) (18)
- Evaluation of implicit formulas for the solution of ODEs (1979) (17)
- Software for modeling and analysis of linear systems with delays (2004) (17)
- Existence and uniqueness for nonlinear boundary value problems (1969) (16)
- Heat Transfer by Conduction and Radiation (1971) (16)
- Stiffness and the automatic selection of ODE codes (1984) (16)
- Global Error Estimates for ODEs Based on Extrapolation Methods (1985) (16)
- Smoothing the extrapolated midpoint rule (1983) (16)
- Boundary Value Problems for Ordinary Differential Equations (1968) (15)
- Existence and uniqueness of solutions of the second order boundary value problem (1966) (15)
- Efficiency comparisons of methods for integrating ODEs (1994) (13)
- Error bounds and variational methods for nonlinear boundary value problems (1968) (13)
- Cheaper integration of linear systems (1973) (13)
- The Effect of Changing the Stepsize in Linear Multistep Codes (1989) (12)
- Some nonlinear boundary value problems (1967) (12)
- Control of local error stabilizes integrations (1995) (12)
- Ill-conditioned matrices and the integration of stiff ODEs (1993) (11)
- Some L2 Markoff inequalities (1965) (11)
- Type-Insensitive ODE Codes Based on Extrapolation Methods (1983) (11)
- Solving ordinary differential equations for simulation (1978) (11)
- R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type (2018) (11)
- Some numerical experiments with DIFSUB (1972) (11)
- Storage Reduction for Runge-Kutta Codes (1979) (10)
- Local error and variable order Adams codes (1975) (10)
- Linear conservation laws for ODEs (1998) (10)
- Difference methods for nonlinear first-order hyperbolic systems of equations (1970) (10)
- Vectorized Solution of ODEs in Matlab (2009) (10)
- Interpolating high-order Runge-Kutta formulas (1990) (10)
- Variable order Runge--Kutta codes (1979) (9)
- Control of step size and order in extrapolation codes (1987) (9)
- Software for ordinary differential equations (1981) (9)
- Diagnosing Stiffness for Runge-Kutta Methods (1991) (9)
- Global error estimation for stiff ODEs (1984) (9)
- Efficient Filon method for oscillatory integrals (2013) (8)
- Locating special events when solving ODEs (1988) (8)
- Stability of explicit Runge—Kutta methods (1984) (8)
- Interpolating numerical solutions of ordinary differential equations (1974) (8)
- Stability properties of Adams codes (1978) (8)
- Existence from uniqueness for two point boundary value problems (1969) (8)
- The Condition of Certain Matrices (1965) (8)
- Rate of convergence of multistep codes started by variation of order and stepsize (1990) (8)
- Asymptotic L2 Inequalities of Markoff type (1964) (8)
- Integrating oscillatory functions in Matlab (2011) (8)
- Starting BDF and Adams codes at optimal order (1988) (8)
- Typical problems for stiff differential equations (1975) (8)
- Numerical Recipes, The Art of Scientific Computing. By W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling (1987) (8)
- On shooting methods for two-point boundary value problems (1968) (8)
- Concentration-dependent diffusion III. An approximate solution (1976) (7)
- Limiting precision in differential equation solvers. II Sources of trouble and starting a code (1978) (7)
- Output in extrapolation codes (1983) (7)
- Variable order Adams codes (2002) (7)
- Interpolation for variable order, Runge-Kutta methods (1987) (6)
- Solving ODEs with MATLAB: Bibliography (2003) (6)
- Fixed vs variable order Runge-Kutta (1984) (6)
- Efficient Extrapolation Methods for ODEs (1983) (6)
- Design of software for ODEs (2007) (6)
- Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systems (1969) (6)
- An inequality of E. Schmidt (1966) (6)
- Solution of structured non-stiff ODES (1986) (6)
- Smoother interpolants for Adams codes (1986) (5)
- Efficiency of a Procedure for Near-Minimax Approximation (1970) (5)
- Monotone Iterations and Two-Sided Convergence (1966) (5)
- Global error estimation with one-step methods☆ (1986) (5)
- Solving ordinary differential equations with ODE, STEP, and INTRP (1974) (5)
- COMPARISON OF SOME CODES FOR THE INITIAL VALUE PROBLEM FOR ORDINARY DIFFERENTIAL EQUATIONS (1975) (5)
- Global extrapolation integrators for solving Sturm-Liouville problems by shooting (1993) (5)
- Exact solutions for concentration dependent diffusion and the inverse complementary error function (1973) (5)
- Weighted quadrature by change of variable (2010) (5)
- Starting variable-order Adams and BDF codes (1987) (4)
- Delay-Differential Equations with Constant Lags (2012) (4)
- Smoother interpolant for DE/STEP,INTRP and DEABM (1983) (4)
- Existence of Eigenvalues of Integral Equations (1971) (4)
- Existence of Solutions for Certain Nonlinear Boundary‐Value Problems (1969) (4)
- Nonlinear second order boundary value problems: Existence and regions of uniqueness (1966) (4)
- On the eigenproblem for displacement integral equations (1968) (4)
- Vectorized Solution of ODEs in Matlab with Control of Residual and Error (2011) (4)
- Solving Volterra Integral Equations with ODE Codes (1988) (3)
- Type-insensitive ODE codes based on implicit A(. cap alpha. )-stable formulas (1982) (3)
- EFFICIENT RUNGE--KUTTA CODES. (1970) (3)
- Discrete least squares polynomial fits (1975) (3)
- Efficient integration of ordinary differential equations by transformation (1988) (3)
- Asymptotic bounds on the errors of one-step methods (1984) (3)
- Efficient use of implicit formulas with predictor-corrector error estimate (1981) (3)
- On a paper of roark and wing (1965) (3)
- Practical improvements to SIMPR codes for stiff ODEs (1989) (3)
- Discrete Variable Methods (2018) (3)
- Solving ODEs with MATLAB: Delay Differential Equations (2003) (3)
- Solving ODEs in quasi steady state (1982) (3)
- Software Based on Explicit RK Formulas (2007) (2)
- Corrigenda: “Limiting precision in differential equation solvers” (Math. Comp. 28 (1974), 141–144) (1974) (2)
- Numerical computations: its nature and research directions (1979) (2)
- Better software for ODEs (1979) (2)
- DDAEs in Control Theory (2004) (2)
- Efficiency of Phase Function Methods for Sturm-Liouville Eigenvalues (1979) (2)
- Estimating the error of the classic Runge-Kutta formula (1994) (2)
- Automatic Solution of Sturm-Liouville Eigenvalue Problems (1978) (2)
- Order Selection in ODE codes based on implicit formulas (1991) (2)
- A type-insensitive ode code based on second derivative formulas (1981) (2)
- Moving averages of solutions of ODEs (2007) (1)
- Solving Sturm--Liouville eigenvalue problems. [SLEIGN, for CDC 6600 computer] (1976) (1)
- Panel Discussion of Quality Software for ODEs (1976) (1)
- Uniformly accurate Sturm-Liouville eigenvalues (1991) (1)
- Linear equations in general purpose codes for stiff ODEs (1980) (1)
- Solving ODEs with MATLAB: Boundary Value Problems (2003) (1)
- Boundary Value Problems for Ordinary Differential Equations. II: Patch Bases and Monotone Methods (2006) (1)
- Parallel implementation of interpolants for Runge-Kutta pairs (1992) (1)
- Stiff Problems (2018) (1)
- Solving ODE'S with Discrete Data in SPEAKEASY (1978) (1)
- A User-Friendly Fortran BVP Solver 1 (2006) (1)
- Convergence of LMM when the solution is not smooth (1989) (1)
- Better extrapolation codes (1985) (1)
- Economical and robust routine for computing sparse Jacobians (1985) (1)
- Solving ordinary differential equations in SPEAKEASY. [SPKODE] (1977) (1)
- Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model (2014) (1)
- Contraction mappings for nonlinear boundary value problems (1968) (1)
- Singular Boundary Value Problems for ODEs L (2003) (1)
- Mathematical software for ODEs. Final technical report (1989) (0)
- Review: Willard L. Miranker, Numerical methods for stiff equations and singular perturbation problems (1982) (0)
- Teaching Numerical Methods in ODE Courses (1997) (0)
- R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type (2016) (0)
- EVALUATION O F I MPLICIT F ORMULAS FOR T HE S OLUTION O F O DEs (1979) (0)
- Error Estimation and Control (2018) (0)
- Mathematical software for ODEs (1989) (0)
- The MATLAB ODE Suite Lawrence Shampine (2019) (0)
- An efficient method for the numerical solution of one-phase Stefan problems (abstract) (1975) (0)
- Software for ordinary differential equations. [Overview of codes available] (1977) (0)
- Book Review: Finite element methods: Fifty years of the Courant element (1996) (0)
- Developing ODE software in new computing environments (1996) (0)
- Over-determined boundary value problems (1968) (0)
- QUADRATURE ERROR ESTIMATES FOR INTEGRANDS WITH MODEST DIFFERENTIABILITY (0)
- Convergence and Stabilit (2018) (0)
- The Computational Problem (2018) (0)
- Basic Methods (2018) (0)
- Variable order Runge--Kutta code RKSW and its performance. [In FORTRAN and FLECS for CDC6600] (1978) (0)
- Runge-Kutta formula with cheap error estimate (1984) (0)
- Neural, Parallel, and Scientific Computations 18 (2010) 195-206 WEIGHTED QUADRATURE BY CHANGE OF VARIABLE (2010) (0)
- Quadrature formulas using derivatives (1965) (0)
- Neural, Parallel, and Scientific Computations 18 (2010) 195-206 WEIGHTED QUADRATURE BY CHANGE OF VARIABLE (2010) (0)
- A NUMERICAL STUDY OF TRANSPORT PHENOMENA IN SPHERICAL GEOMETRY BY THE METHOD OF INVARIANT IMBEDDING. (1970) (0)
- The Mathematical Problem (2018) (0)
- An efficient method for the numerical solution of one-phase Stefan problems (1975) (0)
- Singular ODEs arising from the Laplacian and spherical symmetry (1991) (0)
- New capability for the root solver QN. [In FORTRAN IV for CDC 6600, FUN compiler] (1975) (0)
- Advanced Problems: 5390-5399 (1966) (0)
- Title: Continuous extensions (2011) (0)
- Starting an ODE solver. [Selection of initial step size] (1977) (0)
- Integral equations with transform kernels and the eigenproblemKCx=λx (1971) (0)
- An Inequality for the Derivatives of Nonnegative Polynomials (1966) (0)
- Developing ODE software computing environments (2015) (0)
- Saint Mary ’ s University Mathematics and Computing Science Technical Report 2005 014 A User-Friendly Fortran BVP Solver (0)
- Concerning periodic solutions of y″ + f(t, y, y′) = 0 (1968) (0)
- Automatic recognition of non-stiffness (1982) (0)
- Stability for Large Step Sizes (2018) (0)
- Note on a paper of Bailey and Waltman (1966) (0)
- Solving ODEs with MATLAB: Preface (2003) (0)
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What Schools Are Affiliated With Lawrence Fred Shampine?
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