MATHEMATICS *APP MATH01 C... C... ALTERNATE IMPLEMENTATIONS OF TIME-DEPENDENT DIRICHLET BOUNDARY C... CONDITIONS IN THE NUMERICAL METHOD OF LINES C... *APP MATH02 C... C... DAVIDENKO'S METHOD (A DIFFERENTIAL FORM OF NEWTON'S METHOD) C... *APP MATH03 C... C... THE QUASI STEADY STATE APPROXIMATION C... *APP MATH04 C... C... MULTIPLE STEADY STATES OF A NONLINEAR DISTRIBUTED (PDE) SYSTEM C... *APP MATH05 C... C... 1 + 1 SINE-GORDON EQUATION C... *APP MATH06 C... C... LIOUVILLE'S EQUATION C... *APP MATH07 C... C... FREQUENCY OF THE JACOBIAN MATRIX UPDATING IN DAVIDENKO'S METHOD C... *APP MATH08 C... C... AUTOMATIC UPDATING OF THE JACOBIAN MATRIX IN DAVIDENKO'S METHOD C... *APP MATH09 C... C... A GOOD TEST PROBLEM IN PARTIAL DIFFERENTIAL EQUATIONS FOR THE C... NUMERICAL METHOD OF LINES C... *APP MATH10 C... C... A NEW FINITE DIFFERENCE APPROXMATION OF SECOND-ORDER DERIVATIVES C... WITH NEUMANN BOUNDARY CONDITIONS C... *APP MATH11 C... C... ORDERING OF OPERATIONS IN THE NUMERICAL METHOD OF LINES C... *APP MATH12 C... C... INVESTIGATION OF THE ORDER OF THE EULER AND MODIFIED EULER C... METHODS C... *APP MATH13 C... C... ONE-DIMENSIONAL PARABOLIC PARTIAL DIFFERENTIAL EQUATION WITH A C... TIME-DEPENDENT NONHOMOGENEOUS TERM C... *APP MATH14 C... C... EULER INTEGRATION APPLIED TO INTEGRALS C... *APP MATH15 C... C... INTEGRATION OF BESSEL'S EQUATION OF ORDER ZERO AND ONE C... *APP MATH16 C... C... BESSEL'S EQUATION OF ORDER ZERO (SECOND APPROACH) C... *APP MATH17 C... C... COMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTIONS AND EIGEN- C... VALUES OF A SECOND-ORDER, NONOSCILLATORY ORDINARY DIFFERENTIAL C... EQUATION C... *APP MATH18 C... C... COMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTIONS AND EIGEN- C... VALUES OF A SECOND-ORDER, OSCILLATORY ORDINARY DIFFERENTIAL C... EQUATION C... *APP MATH19 C... C... NUMERICAL INTEGRATION OF THE NORMAL PROBABILITY DISTRIBUTION C... FUNCTION C... *APP MATH20 C... C... LAPLACE TRANSFORM SOLUTION OF SIMULTANEOUS ODES C... *APP MATH21 C... C... TESTING ENERGY CONSERVATION OF ONE-DIMENSIONAL FINITE DIFFERENCE C... OPERATORS C... *APP MATH22 C... C... A COMPARISON OF STAGEWISE DIFFERENTIATION AND DIRECT DIFFERENTIA- C... TION IN THE NUMERICAL METHOD OF LINES - LINEAR CASE C... *APP MATH23 C... C... A COMPARISON OF STAGEWISE DIFFERENTIATION AND DIRECT DIFFERENTIA- C... TION IN THE NUMERICAL METHOD OF LINES - NONLINEAR CASE C... *APP MATH24 C... C... EXPLICIT AND IMPLICIT ORDINARY DIFFERENTIAL EQUATIONS C... *APP MATH25 C... C... EVEN WHEN THE ANALYTICAL SOLUTION TO AN ODE IS AVAILABLE, THE C... NUMERICAL SOLUTION MAY BE MUCH EASIER TO COMPUTE AND USE C... *APP MATH26 C... C... EFFECT OF ODE STIFFNESS ON EXPLICIT INTEGRATOR PERFORMANCE C... *APP MATH27 C... C... LINEAR STABILITY ANALYSIS OF A NONLINEAR SECOND-ORDER ORDINARY C... DIFFERENTIAL EQUATION C... *APP MATH28 C... C... DSS/2 PDE APPLICATION EXECUTED UNDER DASSL WITH SPECIFICATION C... OF THE ODE JACOBIAN MATRIX BANDWIDTH C... *APP MATH29 C... C... ONE-DIMENSIONAL, NONLINEAR, PARABOLIC PDE BY SECOND AND FOURTH- C... ORDER FORMULAS FOR SECOND-ORDER SPATIAL DERIVATIVES C... *APP MATH30 C... C... THE LOGISTIC EQUATION C... *APP MATH31 C... C... A DIFFERENTIAL FORM OF THE HENON 'STRANGE ATTRACTOR' EQUATIONS C... *APP MATH32 C... C... AN ANALYSIS OF THE NONLINEAR STRUCTURE OF THE HENON 'STRANGE C... ATTRACTOR' EQUATIONS C... *APP MATH33 C... C... CRISIS TRANSITION IN THE CHAOTIC LORENZ EQUATIONS C... *APP MATH34 C... C... INTERMITTENCY IN THE CHAOTIC LORENZ EQUATIONS C... *APP MATH35 C... C... ONE-DIMENSIONAL BURGERS' EQUATION WITH DIRICHLET AND NEUMANN C... BOUNDARY CONDITIONS, ILLUSTRATING THE NUMERICAL METHOD OF LINES C... INTEGRATION OF ONE-DIMENSIONAL ELLIPTIC, HYPERBOLIC AND PARABOLIC C... PARTIAL DIFFERENTIAL EQUATIONS (PDES) - EXPLICIT TIME INTEGRATION C... *APP MATH36 C... C... ONE-DIMENSIONAL BURGERS' EQUATION WITH DIRICHLET AND NEUMANN C... BOUNDARY CONDITIONS, ILLUSTRATING THE NUMERICAL METHOD OF LINES C... INTEGRATION OF ONE-DIMENSIONAL ELLIPTIC, HYPERBOLIC AND PARABOLIC C... PARTIAL DIFFERENTIAL EQUATIONS (PDES) - IMPLICIT (STIFF) TIME C... INTEGRATION BY LSODE C... *APP MATH37 C... C... TWO-DIMENSIONAL BURGERS' EQUATION WITH DIRICHLET AND NEUMANN C... BOUNDARY CONDITIONS, ILLUSTRATING THE NUMERICAL METHOD OF LINES C... INTEGRATION OF TWO-DIMENSIONAL ELLIPTIC, HYPERBOLIC AND PARABOLIC C... PARTIAL DIFFERENTIAL EQUATIONS (PDES) C... *APP MATH38 C... C... THREE-DIMENSIONAL BURGERS' EQUATION WITH DIRICHLET AND NEUMANN C... BOUNDARY CONDITIONS, ILLUSTRATING THE NUMERICAL METHOD OF LINES C... INTEGRATION OF THREE-DIMENSIONAL ELLIPTIC, HYPERBOLIC AND PARA- C... BOLIC PARTIAL DIFFERENTIAL EQUATIONS (PDES) C... *APP MATH39 C... C... COMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTIONS FOR A C... FIRST-ORDER AND SECOND-ORDER ODE SYSTEM C... *APP MATH40 C... C... A PARABOLIC PARTIAL DIFFERENTIAL EQUATION WITH INCONSISTENT C... INITIAL AND BOUNDARY CONDITIONS C... *APP MATH41 C... C... NUMERICAL INTEGRATION OF A PARTIAL DIFFERENTIAL EQUATION OVER C... A SEMI-INFINITE DOMAIN C... *APP MATH42 C... C... AN INTRODUCTION TO FINITE INTEGRAL TRANSFORMS C... *APP MATH43 C... C... LSODE SOLUTION OF TWO LINEAR ODES WITH A STIFFNESS RATIO OF 1E+06 C... - PRINTING OF THE NUMERICAL AND EXACT SOLUTIONS C... *APP MATH44 C... C... LSODE SOLUTION OF TWO LINEAR ODES WITH A STIFFNESS RATIO OF 1E+06 C... - PLOTTING OF THE COMPUTATIONAL STATISTICS C... *APP MATH45 C... C... DASSL SOLUTION OF TWO LINEAR ODES WITH A STIFFNESS RATIO OF 1E+06 C... - PRINTING OF THE NUMERICAL AND EXACT SOLUTIONS C... *APP MATH46 C... C... KROGH'S ODE PROBLEM - SOLUTION OF A NONSTIFF CASE BY RUNGE KUTTA C... *APP MATH47 C... C... KROGH'S ODE PROBLEM - SOLUTION OF A STIFF CASE BY LSODE C... *APP MATH48 C... C... BANDWIDTH REDUCTION IN THE NUMERICAL METHOD OF LINES INTEGRATION C... OF PARTIAL DIFFERENTIAL EQUATIONS C... *APP MATH49 C... C... TWO-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATION WITH A MIXED PARTIAL C... DERIVATIVE C... *APP MATH50 C... C... EFFECT OF DISCONTINUOUS INITIAL/BOUNDARY CONDITIONS ON THE C... NUMERICAL METHOD OF LINES SOLUTION OF A TWO-DIMENSIONAL C... PARABOLIC PARTIAL DIFFERENTIAL EQUATION