Computational Mathematics

// Computational Mathematics Framework class ComputationalMathematics { constructor() { this.problems = []; this.algorithms = []; this.methods = []; this.solutions = []; } // Numerical Analysis solveNumerical(problem, method) { const numerical = { problem: problem, method: method, discretization: null, iteration: null, convergence: null, accuracy: null }; // Problem Discretization numerical.discretization = this.discretizeProblem(problem, method); // Iterative Solution numerical.iteration = this.solveIteratively(numerical.discretization); // Convergence Analysis numerical.convergence = this.analyzeConvergence(numerical.iteration); // Accuracy Assessment numerical.accuracy = this.assessAccuracy(numerical.convergence); return numerical; } // Linear Algebra solveLinearAlgebra(matrix, vector) { const linearAlgebra = { matrix: matrix, vector: vector, decomposition: null, solution: null, conditioning: null, stability: null }; // Matrix Decomposition linearAlgebra.decomposition = this.decomposeMatrix(matrix); // Solution Calculation linearAlgebra.solution = this.calculateSolution(linearAlgebra.decomposition, vector); // Conditioning Analysis linearAlgebra.conditioning = this.analyzeConditioning(matrix); // Stability Assessment linearAlgebra.stability = this.assessStability(linearAlgebra.conditioning); return linearAlgebra; } // Optimization optimizeFunction(objective, constraints) { const optimization = { objective: objective, constraints: constraints, algorithm: null, solution: null, convergence: null, optimality: null }; // Algorithm Selection optimization.algorithm = this.selectAlgorithm(objective, constraints); // Solution Process optimization.solution = this.solveOptimization(optimization.algorithm); // Convergence Analysis optimization.convergence = this.analyzeConvergence(optimization.solution); // Optimality Conditions optimization.optimality = this.checkOptimality(optimization.solution); return optimization; } // Differential Equations solveDifferential(equation, conditions) { const differential = { equation: equation, conditions: conditions, discretization: null, integration: null, solution: null, stability: null }; // Space Discretization differential.discretization = this.discretizeSpace(equation, conditions); // Time Integration differential.integration = this.integrateTime(differential.discretization); // Solution Calculation differential.solution = this.calculateSolution(differential.integration); // Stability Analysis differential.stability = this.analyzeStability(differential.solution); return differential; } // Discrete Mathematics solveDiscrete(problem, algorithm) { const discrete = { problem: problem, algorithm: algorithm, complexity: null, solution: null, efficiency: null, correctness: null }; // Complexity Analysis discrete.complexity = this.analyzeComplexity(problem, algorithm); // Solution Process discrete.solution = this.solveProblem(problem, algorithm); // Efficiency Assessment discrete.efficiency = this.assessEfficiency(discrete.solution); // Correctness Verification discrete.correctness = this.verifyCorrectness(discrete.solution); return discrete; } // High-Performance Computing parallelizeComputation(problem, resources) { const parallel = { problem: problem, resources: resources, decomposition: null, communication: null, load: null, efficiency: null }; // Problem Decomposition parallel.decomposition = this.decomposeProblem(problem, resources); // Communication Analysis parallel.communication = this.analyzeCommunication(parallel.decomposition); // Load Balancing parallel.load = this.balanceLoad(parallel.communication); // Efficiency parallel.efficiency = this.assessEfficiency(parallel.load); return parallel; } }